One of the official reasons for the dispute between the early Celtic and Roman churches was the calculation of the date of Easter. Originally, Christians has simply followed the Jewish calendar for the date of Easter. Based on the Bible, John 19, Jesus had been crucified the day before Passover, on 14th Nisan in the Hebrew lunar calendar. Although the calendar is not generally in step with the Julian one that the Christians used, at least it is consistent and undisputed.
However, left to their own devices, the Christians diverged over the details of calculating Easter, with Rome differing from other churches in both the East and West, although as Roman power grew, their system supplanted others. By the 660s, the main dissenting church was the Celtic one in Ireland and Northern Britain. Even there, both versions of the Easter calculations were in use simultaneously, with the result that King Oswy of Northumbria and his wife, Queen Eanfled, held Easter on different days in 665.
The King summoned church leaders to the Synod of Whitby, and after hearing arguments on both sides, decided that the Roman church, with its descent from St. Peter, had priority.
While I have no doubt that both sides firmly believed that their system was right, the affair was more about a ruler attempting to enforce unity in his kingdom. And likewise, the Roman church had more interest in extending its authority across all of Christendom that about the details of theology. (The other crucial matter resoved at Whitby was the monastic tonsure. Celtic monks shaved a strip of hair from front to back, while Roman monks shaved off a circular patch. Obviously, the former had no basis in scripture. But nor does the latter.)
The question of priority via St. Peter was bogus anyway. The Roman church still claims him as the first Bishop of Rome, and says that there is a continuous chain of Bishops linking the Pope of today to St. Peter and hence to Jesus. There is no evidence for the first claim, and the second one is demonstrably false, but that’s their story and they’re sticking to it. In relatively recent years, a genuine first-century tomb was discovered underneath St. Peter’s Basilica, with graffiti and symbols identifying it as the tomb of St. Peter (or, alternatively, of St. Peter and St. Paul). But all that this proves is that the Christians of the time of the graffiti (about 200 AD) thought that St. Peter was buried there. The stories about St. Peter as Bishop are much later than that too.
After the Roman system for calculating Easter had become the standard one, it remained in effect for over a thousand years. It still is, except that the Eastern Christian churches never accepted the Gregorian reform of the calendar in 1582. (Protestants were cautious in accepting this Popish invention too. Britain held out until 1752, when everone changed, except the Inland Revenue, who still celebrate the New Year on 6th April, like the Orthodox churches.)
So, while both Roman and Eastern churches are using the same calculation for the date of Easter, they have different calendars, meaning that on most years, they celebrate Easter at different times. But not this year. This year, it’s Easter in both churches. That would be an ecumenical matter.