I've got both, not sure why folks feel the need to "choose". I liked the Consular story well enough, and the trooper story has been fun. People also complain about the Inq story, but the ending to Act1 was hilarious. My Agent hasn't gotten far, so I assume the story gets better from all the raving I hear. Sith Warrior and Jedi Knight seem sort of "typical" to me, just go do your governments work like any other superman soldier.
So, story is a very subjective thing.
Feel of the quests, I get the vibe from Empire side that the quests are almost comic-villain most of the time, while Republic feels like downtrodden underdog lots of times. In both cases, your forces are almost incompetent and it's all up to you to save the day.
PVP I haven't done, nor a lot of dungeons, but they're server based so I think the real issue there is finding a SERVER to play on, rather than a side.