I am Roman Catholic and what I would like to know is how does the Mass of the Roman Catholic Church differ from one in the Church of Ireland.
Sixty years ago this question would have been simpler. The differences were starker then, but also there was much less diversity within each denomination. Roman Catholic masses were in Latin, many parts were inaudible, and the participation of the congregation was almost entirely passive. Church of Ireland communion services were audible, in English, and the congregation were expected verbally to join in more of the prayers. The Roman Catholic mass was always the Tridentine Mass and the Church of Ireland communion service was very close to the liturgy of Archbishop Cranmer, with minor revisions. Neither had changed very much since the sixteenth century.
Today, the Roman Catholic church (normally) uses the "New Order" Mass produced after Vatican II, within which are several alternatives and options, including a choice between four Eucharistic Prayers (four normally, but actually there are other options in particular circumstances). The Church of Ireland has two orders, a traditional one and a contemporary one. The traditional one (Order 1)is still very close to Cranmer, while the contemporary one (Order 2) is closer, in structure, to the Roman Catholic service. The contemporary one contains many flexibilities , options, "may say" rubrics and "or an alternative" rubrics. It offers a choice of three Eucharistic prayers.
This diversity makes it harder to say what is being compared with what.
In terms of "customer experience" such as style of music (if any), length of homily/sermon, availability of beverages, difficulty in refusing beverages etc., variation exists more within each denomination (and even services at different times in the same building) than it does between the C of I and the RCC.
There are differences between the content and wording of the RC mass and the Church of Ireland equivalent due to different emphases in doctrine between Catholics and Protestants. These can affect, for example, the overall structure of the service, the explicit sacrifice of the already consecrated bread and wine, praying to saints, the prayer about that the bread and wine being for us the body and blood, and prayers for the institutional church.
STRUCTURE - FIRST PART OF THE SERVICE
In the RC mass the penitential rite is at the start, after the greeting. It may consist of a general confession followed by absolution and a Kyrie Eleison (Lord have mercy), or some alternative. After this come the bible readings, the creed and the sermon or homily. Next up are the Prayers of the Faithful (also called the Universal Prayer, Bidding Prayers or Mass Petitions), which pray for the church and the world in general and/or some specific persons or situations. Only after this does the Liturgy of the Eucharist itself begin.
In the traditional order (Order One) of the Church of Ireland service the main penitential rite is not at the beginning of the service, but after the Universal Prayer. However, before the bible readings either the ten commandments, interspersed with the Kyrie Eleison (in English), are read out, or else Christ's summary of the Law from Matthew 22 vv 37=39 is read.
In Georgian times, particularly, the service would not proceed beyond the Universal Prayer, except a few times each year. These normally included at least Christmas, Easter and Whitsun. Even if the service was going to proceed many might leave the church at this point, only those intending to receive the bread and wine remaining. The invitation or exhortation is quite solemn, perhaps emphasising the belief that Holy Communion is not something to be undertaken lightly.
Ye that do truly and earnestly repent you of your sins, and are in love and charity with your neighbours, and intend to lead a new life following the commandments of God, and walking from henceforth in His holy ways, Draw near with faith, and take this holy sacrament to your comfort; and make your humble confession to Almighty God, meekly kneeling upon your knees.
In the Order Two (Contemporary) C of I service the confession may be just after the reading of the Law, or later in the service, and may take various forms. The reading of the commandments may also be interspersed with verses from the New Testament, generally giving a New Testament positive matching the Old Testament negative. For example, "Thou shalt not bear false witness" is followed by "Let everyone speak the truth" (Ephesians 4 25). Another option is for the Beatitudes (Matthew 5) to be read at that point.
STRUCTURE - SECOND PART OF THE SERVICE
The highlight of the liturgy is the Institution Narrative in which the priest tells the story of the Last Supper. This includes the words of consecration "This is my Body" and "This is the chalice of my blood" and "Do this in remembrance of me". There are other prayers both before and after this. In the RC service, and in the Order Two C of I service, there are further prayers after the consecration and before the bread and wine are consumed. In Order One of the C of I the bread and wine is consumed immediately after the Institution Narrative. This places a particular Protestant emphasis on the idea that the sole purpose of consecrating the bread and wine is so people can eat and drink the Body and Blood, and not for any other purpose.
SACRIFICE OF THE CONSECRATED HOST
In the Roman Catholic mass what happens after the consecration, and a proclamation, is that the consecrated bread and wine, by now believed to be the Body and Blood of Christ, is offered to God. The wording varies between the different Eucharistic Prayers. The following is from Eucharistic Prayer One (the Roman Canon):
we, your servants and your holy people, offer to your glorious majesty from the gifts that you have given us, this pure victim, this holy victim, this spotless victim, the holy Bread of eternal life and the Chalice of everlasting salvation. Be pleased to look upon these offerings with a serene and kindly countenance, and to accept them, as once you were pleased to accept the gifts of your servant Abel the just, the sacrifice of Abraham, our father in faith, and the offering of your high priest Melchizedek, a holy sacrifice and a spotless victim. In humble prayer we ask you, Almighty God, command that these gifts be borne by the hands of your holy angel to your altar on high in the sight of your divine majesty.
In the Church of Ireland services God is asked to "accept this our sacrifice of praise and thanksgiving" both in Order One, and in Order Two Eucharistic Prayer One. Eucharistic Prayer Two has only "we proclaim His perfect sacrifice made once for all upon the Cross". In Order One the body and blood have already at that time been consumed, but in Order Two they have been consecrated but not yet consumed.
A little later in the service Order One has we "offer and present unto thee ourselves, our souls and bodies to be a reasonable, holy and lively sacrifice" whereas Order Two has, after the consumption, "Through Him we offer you our souls and bodies to be a living sacrifice".
In all the Church of Ireland versions there is a reference to Christ having already made the perfect sacrifice.
To summarise, in the Roman Catholic services the consecrated bread and wine is offered to God. In the Church of Ireland the congregation, after consuming the consecrated bread and wine, respond by offering themselves. (This last remark refers to the words used in the services, not necessarily the full underlying eucharistic theology of either the RCC or the C of I.)
PRAYING TO SAINTS
In the Confession in the Roman Catholic Mass members of the congregation ask "Mary ever-Virgin, all the angels and saints and you my brothers and sisters" to pray for them. In the Tridentine Mass the confession itself is addressed to God, Mary, Michael, John the Baptist, Peter, Paul, all the saints and the priest, and these same saints are also asked to pray for them.
In the Church of Ireland service saints are not spoken to.
In the RC Eucharistic Prayer One, and in the Tridentine, there is a prayer called the "Communicantes". This is a prayer made "in communion with those whose memory we venerate, especially Mary, Mother of our God and Lord, Jesus Christ, and blessed Joseph her spouse, your blessed apostles and martyrs, Peter and Paul, Andrew (and optionally 21 more saints) we ask that through their merits and prayers in all things we may be defended by your protecting help.
Eucharistic Prayer Three refers to the saints "on whose constant intercession in your presence we rely for unfailing help".
In the Church of Ireland service there is no reference to the merits or prayers of the saints, though in some versions there is a reference to the fellowship of the saints. Reliance on the merits or prayers of the saints is not considered a normal feature in Protestant practice.
PRAYER THE BREAD AND WINE WILL BE FOR US THE BODY AND BLOOD
This is part of the Eucharistic Prayer and so differs depending which version is used. This is sometimes called an epiclesis, that is an invocation of the Holy Spirit.
In the Church of Ireland Order One the prayer is
Grant that we receiving these thy creatures of bread and wine according to thy Son our Saviour Jesus Christ's holy institution, in remembrance of his death and passion may be partakers of his most blessed body and blood.
In the Roman Catholic Eucharistic Prayer One (based on the Roman Canon of the Tridentine mass) the prayer is
Make it spiritual and acceptable so that it may become for us the Body and Blood of your most beloved Son our Lord Jesus Christ.
Neither of these, Roman Catholic or Church of Ireland, specifically requests the involvement of the Holy Spirit (although if in fact His involvement is necessary to the process, then it is implicitly requested). The Roman Catholic one envisages something being done to the bread and wine, whereas the Church of Ireland one is very unclear as to what, if anything, must happen in order that the Body and Blood may be partaken of. This reflects Protestant scepticism as to trans-substantiation, without (in this liturgy) specifically ruling it out, or defining what else might be involved.
In the other three Roman Catholic Eucharistic Prayers God the Father (who is being addressed in the Eucharistic Prayer) is asked to sanctify the bread and wine, by means of the Holy Spirit.
The Church of Ireland Order Two Eucharistic Prayer One says
Grant by the power of the life-giving Spirit that we may be made one in your holy church and partakers of the body and blood of your Son.
This requests involvement of the Holy Spirit but whether He is expected to act on the bread and wine, or on the people, or both, or in some other way altogether, is unspecified.
The involvement and invocation of the Holy Spirit is regarded as very important by the Eastern Orthodox churches. If in some respects the Catholic and Protestant services are closer than they once were, in this respect there is something of a rapprochement with the East.
Roman Catholic masses contain, in the Eucharistic Prayer, a prayer for the peace and unity of the church, with specific mention of the Pope and the bishop. Other prayers for the world and the church are often made in the Universal Prayer also called Prayers of the Faithful. In the Order Two Church of Ireland service similar prayers, which would not normally mention the Pope, are made at the same point of the service as the Prayers of the Faithful, which are called in the Church of Ireland service "intercessions". In Northern Ireland the Queen is normally mentioned, though not in the Republic of Ireland. There are several optional suggested patterns for the C of I Order Two intercessions which all mention bishops and clergy before the Queen (or in the Republic the President) and civil authorities, but these are only suggestions.
The Order One Church of Ireland service has its own Universal prayer which begins "Let us pray for the whole state of Christ's Church militant here in earth". After praying that the universal church be inspired with the spirit of truth, unity and concord it continues
We beseech thee also to save and defend all Christian Kings, Princes and Governors; and especially thy servant Elizabeth our Queen, that under her we may be godly and quietly governed; And grant unto her whole council, and to all that are put in authority under her, that they may truly and impartially minister justice, to the punishment of wickedness and vice, and to the maintenance of thy true religion, and virtue.
(This is the version the C of I uses in Northern Ireland, there is a modified form for use in the Republic.)
Give grace, O heavenly Father, to all Bishops and Curates, that they may, both by their life and doctrine, set forth thy true and lively word and rightly and duly administer thy holy sacraments.
This reflects a view of the institutional church, the bishops and clergy, as simply one facet of the Christian community, whose functions are preaching the word and administering the sacraments. In the worldview expressed in Order One the civil authorities are no less part of the church, and their particular functions are to ensure justice and to maintain true religion. A lower view of the importance of the church hierarchy is common in Protestantism. The increase in secularism, and the growing presence of non-Christian religions, is perhaps a challenge to such a view.
The Roman Catholic Mass (ordinary form can be seen here.
The Roman Catholic Extraordinary form with English translation can be seen here.
The Church of Ireland services are on this site but it is necessary to scroll down. Holy Communion One is Order One and Holy Communion Two is Order Two.
The Bishop of Down and Dromore, Rt Rev Harold Miller, who was involved in the C of I liturgical revisions of 2004, has written about them here.