Both the old and the new coincide on moveable feasts because they're connected to Pascha. So we celebrate Lent, Holy Week, Pascha, Ascension, Pentecost, and the beginning of the Apostle's Fast at the same time.
They differ at the immovable feasts, which would involve the daily saints, Dormition, Nativity, Annunciation, the end of the Apostle's Fast, the beginning of the Liturgical Year, etc. by 13 days.
The fact that we're on different calendars bothers me a little. But it's also noteworthy that because of it, the Liturgy is celebrated on more days of the year.
My Godsister's patron saint is St. John of San Francisco, who reposed on July 2, 1966 in America on the real-world (with which the new calendar coincides) calendar everyone in America uses. Of course, he was on the Old Liturgical Calendar, so according to that, he reposed on June 19th (the day of my patron saint).
So you'd think our new calendar GOAA parish would celebrate him on July 2, right? Nope...we celebrate him on June 19. Of course, on the old calendar, St. John of SF did repose on St. Jude's feast day, so the GOAA may have chosen to connect him with St. Jude...especially since St. Jude figures a little into St. John of SF's story.
But it's still confusing.