Ever wonder how a battle between the United Federation of Planets and the Galactic Empire might play out? Wonder no more. Here's why the Federation (Star Trek) would defeat the Empire (Star Wars) without even breaking a sweat.

1. Cloaking technology - advantage Federation. Yes, Kirk and Spock stole this from the Romulans, but that only goes to show they're better spies, too.
2. Transporter technology - advantage Federation.
3. Logic - advantage Federation (no Vulcans in the empire).
4. Artificial intelligence - advantage Federation. Sorry, R2D2, but you're no Data.
5. Time travel capability - advantage Federation.
6. Navigational prowess - advantage Federation. Yes, Han Solo is a decent improvisational pilot, but he doesn't stack up against Data, Dax or Sulu; besides, when did he ever engineer a trip to the past by attempting a slingshot maneuver around a star?
7. Weapons capabilities - advantage Federation. Comparing a light saber to a phaser is like comparing a broadsword to a machine gun. That's not to mention photon torpedoes, quantum torpedoes and the potential doomsday use of the Genesis device. Two words that would be enough to make Vader soil that plastic-plated "armor" of his: Locking phasers. 
8. Tractor-beam technology - advantage Federation. Just lock onto that Death Star and haul it into the nearest black hole.
9. Empaths - advantage Federation (no Betazoids in the empire).
10. Diversity - advantage Federation (more than 150 member worlds vs. lookalike storm troopers).
11. Bad-ass warriors - advantage Federation. Can you name a single member of the empire who could stand up to a Klingon warrior with a bat'leth? Or without one, for that matter? Jar-Jar Binks, maybe? Jabba the Hutt? I think not. The Federation could also call on Mr. Spock, Kira Nerys, Jadzia Dax, Hikaru Sulu and others who are quite skilled at physical combat.
12. Shield (force field) technology - advantage Federation. Two words that should strike terror into the heart of anyone aboard the Death Star.
13. Medicine - advantage Federation. Let's see: McCoy, Crusher, Phlox, Bashir, Pulaski, EMH (The Doctor). Do they even have physicians in the empire, let alone tricorders? How about dermal, bone and cellular regenerators? Thought not.
14. Financing - advantage Federation. The presence of a Ferengi (Nog) in Starfleet and another (Quark) on a Federation space station gives the Federation a definite edge in terms of raising enough gold-pressed latinum to finance the very short war that would be needed to force the empire's surrender.
15. Engineering expertise - advantage Federation. Does the empire have anyone approaching the skill levels of Montgomery Scott, Geordi LaForge, Miles O'Brien, B'Elanna Torres or Trip Tucker? Does it even have engineers at all, or is everything held together with duct tape and the Force?
16. Holodecks/suites - advantage Federation. Great venues for everything for combat training to R and R. Nothing like that in the empire.
17. Quality of opposition - advantage Federation. Starfleet has faced off against the Borg, Klingons, Romulans, Andoreans, Jem'Hadar, Changelings, Cardassians, rogue Vulcans, genetically engineered humans, crystalline entities, Xindi, time-traveling Suliban, Mirror Universe alter egos. ... I'll stop there. Talk about opportunities to hone your skills. The empire lost its shirt at the hands of the Rebel Alliance, which would be like the Maquis conquering the Federation. Um, no. Not gonna happen.
18. Leadership - advantage Federation. I'll take Sisko, Kirk, Picard, Archer, Janeway, Spock, Data, Sulu, Scotty, Dax, etc. over Vader's posturing and Palpatine's bloated arrogance any day. I'll also take Spock's logic over any Jedi's nebulous talk about the Force without hesitation.
19. Space travel - advantage Federation. Starfleet has multiple classes of starship featuring creative designs, not to mention space stations, runabouts, shuttles and so forth. Most Star Wars ships, by contrast, look like glorified USAF fighter jets or battleships floating out in space. Starfleet ships also come equipped with warp drive, and Deep Space Nine offers immediate access to a wormhole. We're looking at a fleet of Ferraris and Porsches standing next to a bunch of rickshaws and Model-T's.
20. Natural abilities - advantage Federation. Yes, Jedis can wield the force, but that's no match for Q, who, despite his mercurial nature and propensity for creating obstacles, always seems to have the Federation's back when it's most needed. And if Starfleet managed to locate and enlist the help of Kevin Uxbridge ... well, do you really mean to suggest that Palpatine or Vader would be any match for a Douwd? 

The fate of the Galactic Empire would be decided the moment Picard said, "Make it so," and the war would be over faster than a replicator could deliver a steaming cup of Earl Grey to his eagerly waiting hands.