I've always thought that Star Wars tech is pretty inferior, so Treknology would stomp all over their stuff. Unless, one or more fairly powerful Force users were in play. They would own the day, I think. Unless unless, a transporter operator got the drop on them and scrambled them all over the place. I'm thinking a Force user *might* be able to hold themselves together if they knew what was happening, but given that there are no transporters in Star Wars, they might get taken out before they knew what hit them.The problem with a crossover is no matter how it ends, some fans are going to be angry their side didn't kick the other's ass. The best you'd get is a stalemate.
The way I see it is this: (note...personal opinion only)
Star Trek might deal in hard numbers (5.1GW for a Type X phaser, 50 isotons for a photon torpedo, etc), but Star Wars does not....this leaves Star Wars pretty open to just how much power a turbolaser on a Star Destroyer, or even a Corellian Corvette has in comparison to a Star Trek TNG phaser. For all we know, a turbolaser could be every bit as powerful as a Type X phaser. The material integrity in the construction of an Imperial Star Destroyer or Corellian Corvette might be the same as a Galaxy or refit Constitution class starship. Just because it has the word "laser" in it (granted, in Trek terms, a laser is less powerful than a phaser), does not mean it is inferior. In the Star Wars universe, the term "laser" is a generic catch all term for blaster or beam weapons.
Star Destoyer shields are generally planetary strength, or near planetary strength. It could take a Type X phaser a bit to cut through the shields.
(Besides, some Star Wars ships have ion cannons that ignore shields and can disrupt/disable targeted ships' systems...and sorry, I don't count the whole "if it didn't happen on screen" crap. Lucasfilm Archives--since the mid 80's-- says the ships have 'em, they have 'em....and in my tribute films, they use 'em. )

But ultimately, to satisfy (or disgruntle) either and both fanbases, the best to be hoped for is a stalemate...or a fanfilm with alternate endings...one as a tie, one favoring Star Trek, and another favoring Star Wars.
