The amount of Latinizations is not really a matter of Church-to-Church, but more like parish-to-parish. It is possible to find Ukrainian, Romanian and Ruthenian Catholic parishes that are extremely “Orthodox” (sometimes more “Orthodox” than the Orthodox themselves), and it is likewise possible to find Melkite Catholic parishes that are heavily Latinized. So, as others have pointed out, it is hard to generalize. On an official level the Melkites and the Ukrainians seem to have been the most outspoken about maintaining our Orthodox roots, as well as returning to them where we have allowed Latin influence to replace our heritage. The Romanian Greek Catholic Church here in the U.S. is so small that often times not many people know what’s going on with it. I know that Bishop John Michael is a firm believer in restoring the Byzantine heritage where it has been supplanted by Latinization, but I also understand that he has been fought tooth-and-nail by a number of his parishes that are comfortable in their Latinizations. One must be pastoral about these things and not rock the boat too much at one time lest we cause scandal to our faithful.
I would also like to point out, however, that it is also easy to find Orthodox parishes that are Latinized. The Greek Orthodox parish up the street from me has a number of Latinizations. Although I’m by no means a supporter of the Latinization of the Eastern Catholic Churches, I am curious as to why it seems to be no big deal when the Orthodox Latinize themselves.