If I attend Mass on Ascension Thursday in my diocese that observes Thursday & travel to a diocese that transfers to that Sunday, do have Sunday obligation since the liturgy will be the same?
Yes. Every Sunday is obligatory unless a particular dispensation applies. The particular Mass text doesn't matter. You can meet your obligation by attending a Nuptial Mass, a Funeral Mass or a Votive Mass as long as it is celebrated that day (or the evening before).
Can. 1246 §1. Sunday, on which by apostolic tradition the paschal mystery is celebrated, must be observed in the universal Church as the primordial holy day of obligation. The following days must also be observed: the Nativity of our Lord Jesus Christ, the Epiphany, the Ascension, the Body and Blood of Christ, Holy Mary the Mother of God, her Immaculate Conception, her Assumption, Saint Joseph, Saint Peter and Saint Paul the Apostles, and All Saints.
Can. 1247 On Sundays and other holy days of obligation, the faithful are obliged to participate in the Mass.