I was interested in the topic myself, so I did a little research while ago.
Sifting through all the materials, and trying my hardest to get through the bias that each fanbase provides (I'm a Star Trek fan BTW), I think the issue is best depicted in this YouTube video:
[youtube]hNxhrPaaCA4[/youtube]
Basically, I believe Galaxy-class starships can hold their own against the larger Imperial battle cruisers, but both fanbases agree that the Death Star would be tough to beat as its weapon is the more powerful than anything else. Also, the Empire had a higher number of troops at its peak while the Star Trek beings would have to collaborate.
Based on the Wikipedia entry on the matter (some people just have too much time on their hands)
HERE , Star Wars is given the advantage mainly based on a book by physicist Dr. Curtis Saxton who estimated the power of weaponry of Star Wars vessels to be far greater than any Star Trek vessel provided. I guess the homerism in me disputes this book given that LucasFilm hired the man and Saxton acknowledged many "Warsies" in his book. Can you say slanted?
Personally, I wouldn't mind if the Empire would wipe the Alpha Quadrant off the face of the universe; Star Wars and Star Trek are two entirely different franchises that has different aims and tastes.