On the surface level, the exterior level, I would say that "Easternness" (for lack of a better word) varies from parish to parish and person to person, due to three factors: (1) what does it mean to be both correct and universal, i.e., orthodox and catholic; (2) the history of latinizations in the Eastern Catholic churches; and (3) in the U.S., certain controversies that arose regarding priestly celibacy.
On a deeper level, I think the crucial issue is theosis. And, I think that theosis can take place in different forms but is one in essence. So, for all of us -- Roman Catholics, Eastern Catholics, Chalcedonian Orthodox, non-Chalcedonian Orthodox-- theosis depends on the human heart and its openness to the grace of the Trinity.
That's just my two cents' worth of thinking, and I am just a sinner.
-- John
