Alright, i play on the server The Black Vulkars. But have made 2 characters on 2 other servers both being pvp. I made empire and republic on both servers just to check if it was just my server with the problem. The Black Vulkars average there where 2.7 empire to 1 republic. The next server was worse being 3 empire to 1 republic, and the next was the same as the first server i mentioned.
Basically i think this works to the republics advantage.
1. Little if not no pvp que wait time.
2. Not too much competition for quests/kills.
3. Guilds aren't jam packed with a bunch of random invites, and are very picky about their members. (Mature people or players who actually are good at their class)
Downsides
1. World pvp your outnumbered. (which world pvp doesn't happen all that often anyways)
2. Less pre-made pvp groups.
3.The empire most likely have more people buying and selling on the Galactic Market, due to their numbers.
If someone plays empire because they don't want to be a "goody two shoes" or "The good guy" This is how you can tell they are the immature party of the empire. and vice verse, but if you've looked on other sites and even on these forums, the majority of the people saying i dont play the other side because they are "good/bad guys" is so far from the 6+ hours of reading forums myself is 7 empire players to 1 republic.
Minus the RP servers a rough estimate on my own experience and other players on forums and google. Averages out to 7 out of 10 players are Empire.
I do play both Empire and Republic.... but on my server i have to wait till 1:00AM-5:00AM to even play without having the trouble of fighting to kill a whole group of mobs by myself without someone tagging a mob in that group. <--Talking about empire on my server.
Hope this helped a little