Let's line up the all-stars of each universe and see how they match up, shall we?
STAR WARS:
Death Star
The Empire
The Force
Jedi
STAR TREK:
Q
Cloaking Technology
Transporter Technology
Borg
Q is disqualified in my opinion, heck, if there ever was a battle between the two universes, Q would probably be the one to cause it in the first place. If we take the remaining elements, I think we come pretty close to a draw. While SW definitely has a huge advantage with the more powerful weaponry, not to mention The Force, Jedi and all that entails, ST holds key tactical advantages in Cloaking and Transporter technology. The usefulness of cloaking your ship is self explanatory and transporter technology could be used to instantaneously board your opponents ship.
I think it would be a very long war and possibly end up in a stalemate.
STAR WARS:
Death Star
The Empire
The Force
Jedi
STAR TREK:
Q
Cloaking Technology
Transporter Technology
Borg
Q is disqualified in my opinion, heck, if there ever was a battle between the two universes, Q would probably be the one to cause it in the first place. If we take the remaining elements, I think we come pretty close to a draw. While SW definitely has a huge advantage with the more powerful weaponry, not to mention The Force, Jedi and all that entails, ST holds key tactical advantages in Cloaking and Transporter technology. The usefulness of cloaking your ship is self explanatory and transporter technology could be used to instantaneously board your opponents ship.
I think it would be a very long war and possibly end up in a stalemate.