Yes and no. If you take those concepts in Christianity that are close to the four you list and break them into parts, then the difference will be seen.
The parts are ideas (the Word), emotional response, will, spoken words and actions.
Christians share a common set of writings (though interpreted with variations) that influence common ideas.
Being human and responding to the same Holy Spirit, the emotional responses will be similar.
An act of the will is dificult to quantify and compare, except in its results.
Because of different faith traditions, the words and actions that flow from the common ideas differ. Thus you will not have uniform prayers, meditations or emphases among the different Christian groups and individuals within them as they work out the intent of the words.
The similarities are most pronounced in the ideas then.
Metta (loving kindness): wishing the happiness / well-being of all conscious beings.
Christians are called to love our enemies (Matthew 5:43-48) and "If it is possible, as far as it depends on you, live at peace with everyone." (Romans 12:18)
21 If your enemy is hungry, give him food to eat;
if he is thirsty, give him water to drink. 22 In doing this, you will heap burning coals on his head,
and the Lord will reward you. (Proverbs 25:21-22)
Karuna (compassion): wishing the end of suffering for all conscious beings.
Compassion is commanded of all:
3 Praise be to the God and Father of our Lord Jesus Christ, the Father
of compassion and the God of all comfort, 4 who comforts us in all our
troubles, so that we can comfort those in any trouble with the comfort
we ourselves receive from God. (2 Corinthians 1:3-4)
8 Finally, all of you, be like-minded, be sympathetic, love one
another, be compassionate and humble. (1 Peter 3:8)
However, suffering is also taught to be beneficial to the soul, as exemplified by Job and others. The primary goal is not the alleviation of suffering, but the alleviation of sin, its cause.
Mudita (sympathetic joy): rejoicing when a conscious being (oneself or other) is experiencing well-being (the opposite of envy).
15 Rejoice with those who rejoice; mourn with those who mourn. (Romans
Upekkha (equanimity): "To practice upekkha is to be unwavering or to stay neutral in the face of the eight vicissitudes of life—which are otherwise known as the eight worldly winds or eight worldly conditions: loss and gain, good-repute and ill-repute, praise and censure, and sorrow and happiness". I understand that it is also associated with the ability to stay in the present moment, in a state of serene mindfulness.
First, Job displayed this character:
“Naked I came from my mother’s womb,
and naked I will depart. The Lord gave and the Lord has taken away;
may the name of the Lord be praised.” (Job 1:21)
Second, Solomon spoke about the importance of living in the "House of Mourning" not the "House of Pleasure". He also urged moderation in all things:
Do not be overrighteous,
neither be overwise—
why destroy yourself?
17 Do not be overwicked,
and do not be a fool—
why die before your time?
18 It is good to grasp the one
and not let go of the other.
Whoever fears God will avoid all extremes. (Ecclesiastes 7:16-18)
This extends to the pursuit of wealth.
Keep falsehood and lies far from me;
give me neither poverty nor riches,
but give me only my daily bread. (Proverbs 30:8)