I honestly think that this is an impossible question to answer, as all questlines (that I've gotten anywhere in) have really different feels. Again, I haven't gotten all that far on many of these, but, here's my take:
Empire side:
Sith warrior appeals to those who want to be the awesome, bad ***, head of the galaxy. You're the chosen one. You're worshipped, feared, and adored. The storyline more or less comes down to this. You don't need to be clever or crafty as you're a freaking Sith. EVERYTHING can be solved with a lightsaber.
Sith Inquisitor: You have to be a lot craftier than the warrior. You're an underdog, but still an underdog with mystical powers. (Someone I know compared this to playing Tabris after Cousland in DA:O). There are more twists and turns, and more of an underdog feel.
Bounty Hunter: You really are just after the money. (Or possibly revenge.) It's not a super subtle story, more the feeling I've gotten is that you're out to either make money, kill those who bother you, or both. Great for when you just feel like killing something.
Imperial Agent: This is really a story for masochists. From the moment my agent got off the couch after her affair with Master Tlan, looking pained, I should have grasped that things were going to end up poorly. A few torture sessions, **** threats, and psychotic episodes later I *really* should have gotten the message. If you're okay with that, though, it's a complicated story where eventually everything makes sense. (Sort of. Maybe. If you totally over analyze. It's the kind of story that appeals to people who freaking over analyze everything.)
Republic Side:
Jedi Knight: You are Superman, the ultimate hero, saver of puppy dogs and kitty cats. People turn on you, but in the end, you defeat them as they were *bad guys*. And you totally save the galaxy, as you're the good guy.
Jedi Counselor: Slightly more shaded than Jedi Knight, but you can still be sweetness and innocence personified. (Or a Machievellian schemer, when the choices allow you. Sadly, not as often as I'd like.)
Trooper: Seriously, you are Commander Shepard from Mass Effect. If that's okay with you, it hasn't been bad so far. But like...that's what you are. With a gung ho supporting cast who all seem drawn from the pages of super nationalistic comic books. One of my friends loves this storyline, but does admit that it's pretty straight forward "kill the bad guys".
Smuggler: You want hard cash, and you want it now. Whether you're the cad with a heart of gold, or just after a good pay out...that's pretty much what you are.
Again, I could be mistaken as I've only gotten far past the prologue on agent (which I've finished). But it's enough to be pretty sure that different classes appeal to different people. I almost can't make myself finish bounty hunter - while I keep itching to roll a second agent (and really want to finish trooper and counselor). There's a different flavor to all of them, though, so which is "best" seems kind of silly, as I know people who rave about each storyline (and those who hate each). It seems to be more of a "what fits your own personality" type thing.