i don't think the difference is very major... i beleive we beleive Mary died before the 'assumption'... i'm not clear on the Catholic thoughts on it...
Orthodox thoughts:
Dormition
The Dormition of the Theotokos
The Dormition (Falling Asleep) of the Theotokos is one of the Great Feasts of the Orthodox Church, celebrated on August 15.
The Orthodox feast of the Dormition is very similar to what Roman Catholicism calls the Assumption of Mary. According to Orthodox Tradition, Mary died like all humanity, "falling asleep," so to speak, as the name of the feast indicates. (Roman Catholic theologians are divided on the issue of whether Mary died. Today most would favor an actual death before the Assumption.) The feast is preceded by 14 days of fasting; on these days, either the Great Paraklesis (service of supplication) or the Small Paraklesis is celebrated.
The Apostles were miraculously summoned to this event, and all were present except Thomas when Mary passed from this life. She was then buried.
Thomas arrived a few days later, and desiring to see her one more time, convinced the others to open her tomb. Upon doing so, the Apostles discovered that her body was no longer present. This event is seen as a firstfruits of the resurrection of the faithful that will occur at the Second Coming of Christ. The event is normally called the Dormition, though there are many Orthodox parishes in English-speaking countries with the name Assumption. In Greek, Dormition is Koimisis—falling asleep in death—from which the word cemetery derives.
The dormition of the mother of the Theotokos, the Righteous Anna, is celebrated on July 25.
http://orthodoxwiki.org/Dormition
My untutored opinion is that we're agnostics on whether Mary died. To ME the big deal is participation in eschatological fulfillment.