No, that's not correct. The Orthodox ordain married men to the parish priesthood. That's different from "allowing priests to marry". Once an Orthodox priest is ordained, he cannot remarry and remain an active priest, even if his wife dies.
Orthodox bishops are all celibate; they are typically recruited from monasteries.
Western (Latin Rite) Catholics traditionally have not ordained married men to the priesthood. Eastern (Byzantine Rite) Catholics do, just like the Orthodox, although not typically in the US (for political reasons).
OK, I misspoke, Orthodox Priests can be married, and indeed, most Orthodox priests are. I know several since I have many Greek friends here in the city.
But an Orthodox priest can’t marry while a priest. If he wishes to have a family life, he must get hitched BEFORE he is ordained to the deaconate, the penultimate step before becoming a priest.
I bring this up because of the ongoing debate within Catholic circles—pushed energetically by the Church’s internal and external critics—about whether to revoke the rule requiring priest celibacy. The regulation was formally established at the Council of Trent in 1563 after centuries of controversy over the issue of priests and marriage.
Prior to Trent, the Catholic Church took the same approach to the question of priestly marriage as the Orthodox Church did (and does today). If the priestly celibacy were no longer required, the Catholic Church would likely return to its former practice.
Its ok for the Byzantine Rite Catholic Priests to be married. Back in the day, the Romans insisted Byzantine Catholics dont marry as a condition for being allowed to create their own BC parishes...or so I was told.
John Paul II gave the green light for BC priests to get married as a directive to return to the way things were done in the BC in the old country. You will also see infants getting communion now in the BC as well.