Turrets are faster on imperial.
Shock does damage instantly, throw a rock does damage at the end of the GCD.
DIRTY KICK MAKES YOU BALANCE ON ONE FOOT and stand still while you kick. Electro-knife is a drive-by stun.
Dailies are 100 times easier to complete on empire than on republic. (you can just run to the end and practically solo the 4man heroics on empire side)
I'm sure there is more.
My main is imperial and I feel pretty bad for republic. Harder dailies, crappy players, boring armor, skill imbalance on what are supposed to be mirrored classes.....
The only big advantage I've noticed for republic is on alderan map left = spawn left so you don't have the confusion you have on imperial when telling people to go left and right at the start.