ok ok I have decided to join this discussion. I am a fan of both Star Wars and Star Trek, but I favor SW a bit more. Here are my ideas on how this would play out.
Star Wars wins this hands down. Ih you take into account the books, comics, videogames, The Empire has much more resources than the Federation, Borg, Klingons, Romulans, and all others combined. Someone mentioned the Death Star, there are actually 3 Death Stars, not to mention the Eclipse Class Star Destroyer from Dark Empire, which features a main weapon modeled from the Death Star's superlaser. Star Trek simply could not begin to match the sheer numbers and firepower at Lucas' disposal.
Borg what? The Empire simply destroys their home planet with wave upon wave of Tie Fighter bombardment or simply a light blast from the Death Star. Same goes for any other species homeplanet. The rest is simple mop up.
If the Borg decided to assimliate any Jedi, they would immmediately turn to the Dark Side, being mostly machine, and become pawns of either The Emperor or some other Sith Lord. The Borg are doomed in this battle.
The hero's of Star Trek may figure out a way to neutralize the
groan Midichlororians but I am sure that Deanna Troi or Geordi would fuck this up somehow
Q? No not really a factor here, the Q care not for the well being of the galaxy, maybe a slight interest in Jean Luc Picard. I fear Picard would be assassinated long before the end of this battle. How many times has his crew been brainfried by some whack alien race, they stand no chance against the hordes of Dark Jedi.
In the end the Dark Side of the Force wins this and any battle.