So, I started out on Repbulic side because I have family that plays there and I wanted to hang with them. They started before me, so I'm still playing catch up, since I have limited play time.
However, I live in Tokyo (they are in the U.S.) and the game gets really dead when I can play, which is generally when U.S. peeps are sleeping, except mornings on weekends, when I can play prime time in the U.S.. I would log in and go to the fleet hoping to find a flashpoint, and there would be maybe 12-20 people on many times. I would try for a half hour to an hour to get a group, then give up and go solo. Forget trying to get groups for heroics on a planet.
So, I made an alt on Empire. Usually about 3x as many people on even during my odd hours and I've had no problem running flashpoints. So, now I play my republic toon on weekends, and my Imperial the rest of the time. But apart from the time issue that hits me, I see a lot of reasons why Empire outnumbers Republic.
1) Ability delay - mortar volley vs. death from above. Instant lightning, or delayed tossing big rock, etc. I can see the arguments that since it is less than a GCD, it doesn't matter so much, but it sure feels like it does. Seems to me in playing that if I get off my attack instantly, often mob is dead sooner, and saves me from at least some damage. PvP can be even bigger. Putting every single delay on the Republic side was just a glaring miss.
2) Gear/Fashion. Yes, I understand there are lore issues, but a poo brown robe vs. some of the cool sith outfits? Game, set, match to the Sith! Ok, the smuggler has a really cool look if you can ever find the hat and duster, but the rest, all fashion points go to the empire.
3) Story: Ok, I am enjoying the story with my jedi shadow and my low level smuggler and trooper, but the story on Empire just seems to be more dramatic. I like my Empire side companions better, too, mostly. For example, not sure why I get stuck with a healer that hates the force on my jedi shadow tank. Tell him to go heal a freaking trooper, or something.
Bottom line - there are more people on Empire side because its just done better. It looks, feels, and plays better than Repbulic, and now it just perpetuates the imbalance because people flock to the side where they can get groups more easily (well, apart from PvP, anyway).
Gimmicks aren't going to fix the problem - the designers have to pay some attention to the above points - though I'm sure there are others - if they want to fix the imbalance.