Having a Roman Catholic father and an Eastern Catholic mother, this is what I see as differences and similarities:
In many Byzantine Catholic churches, they have shortened the Liturgy. After the first litany, they might move on to the Gospel readings and then the Eucharist. In my Orthodox church, there are 2 more litanies. Also, in the Byzantine Catholic churches, they might not have people come up to venerate the cross after every Liturgy, this seems to be reserved for special occasions where you get oil on your forehead. Another difference is they have seemed to cut out the singing of "In Health and Salvation... God grant them many years" at the end of every Liturgy. This also is reserved for special occasions. In my Orthodox church, this is sung every Sunday.
Also, in Byzantine Catholic churches in America, you get many Roman Catholics visiting and also Roman Catholic priests who are biritual so there might be more of a blending of Roman Catholic practices into Eastern Christian ones, such as the Divine Mercy chaplet. However, this doesn't seem to be worked into the actual Liturgy, it might be a practice outside of the Liturgy.
One point I want to make is that the Byzantine Catholics are not Italian Roman Catholics who put on the cloak of Orthodoxy to trick the Orthodox into being duped into falling under the Pope's control. They were Orthodox Slavs from the very beginning and for whatever reason went under the Pope. So, they have the tradition of Orthodoxy and have done a pretty good job of keeping it intact in the face of modernism.
One thing that does bother me is when Roman Catholics think that if you are interested in Orthodoxy that you should just be Eastern Catholic and that there is no difference other than being under the Pope. There is a difference is theology between the East and West. However, that is from the Roman Catholic viewpoint. The Eastern Catholic viewpoint does put their focus on the theology of the East, Christian mysticism and on Patristics.