I have played 7 of the 8 Stories, a couple of them more than once...
Imperial Agent is by far the best story in the game. You could play it 3 times over and come out with different playthroughs and endings. It has tons of action, twists, and drama, and even a few laughs to lighten up the mood. On top of this, all of the companions have a very distinct personality that you very much get attached to as each gets involved in some way and doesn't just feel like they were "tacked' on. You have an insane amount of NPCs in the story that allow for different outcomes in how you develop your adventure.
A very close second (and I mean VERY close) is the Sith Warrior story. It has by far the greatest antagonist of any story in the game. Your choices very much feel like they matter, though on a slightly lesser scale than the Agent's story. A Light Side play through feels very epic in the sense that you constantly push against all the ideals of the Sith way, while a Dark play through just makes you feel like an utter God of War. A couple companions feel like they are just ...there, but several actually are involved heavily in the story, including one that is completely different depending on whether you play Dark or Light Side.
Smuggler is my choice for the third best story, and it's based solely on just the very entertaining dialogue through out the game. No other class story plays out in such a witty way that you get a smile out of almost every cutscene. While only Act 1 of the Smuggler story actually felt like it was important and the second two acts more tacked on for content, the writing of the story itself drives the enjoyment factor through the roof as you constantly want your Smuggler to say quite possibly the coolest lines the game has to offer. Some of the companions I couldn't care less about, but there was enough influence on the key Companions that made me at least feel attached to them. Sadly, the best antagonist of the Smuggler story is removed early, and you really don't care as much about the secondary ones.
Some may disagree with me here, but my pick for 4th best story is the Trooper. Act 1 is incredible in my opinion. The whole betrayal plotline, while cliche, makes you really want justice and draws you into the plot quickly. The companions themselves have a very low involvement in the story save for a few parts, but their personalities were extremely likable. It might be because I am former military, but while most of my guildies that played the Trooper story disliked it as a whole, I actually enjoyed it. If you are more chaotic or evil, you probably won't enjoy the Trooper the way it was designed to be played. This is a story definitely designed for a Light Side play through and not as a Dark Side thug.
The Bounty Hunter is in many ways equal to the Trooper to me. I played Light Side, which felt like a Space Opera of the Kind Hearted Hunter with morales just looking to make some cash, but generally just breaking even. The Dark Side looks to be more about playing the Thug role who would sell his momma for a dime. One thing I did like about this story is that it feels the most NEUTRAL to alignment of Empire v. Republic. You literally are aligned with the Empire solely for story purposes only, and not because you like the Empire, which is great. It definitely feels like at some point they could set up a cross faction switch and allow players to change allegiances just solely on how the Hunter plays out. My biggest beef with the story, and the reason it's lower than the 4 above it, is that the story is literally, "Go to this planet, collect this Bounty" for practically the WHOLE THING. The companions kind of feel out of place to me. I don't think of a Hunter having a crew, and so these people that tag along with you just don't feel like they belong. Most people can't even name a companion for the Hunter other than Mako or Blizz as it is.
#6 & #7
I couldn't choose which of these felt better, so they tie for worst in my opinion. The Consular Story was weak... like, really weak. I couldn't get into it at all, as it doesn't engage you at all through out the prologue. I was practically bored to death all through out Tython, which probably led to me never getting into the story at any point. The companions were extremely disinteresting as well, with the possible exception of Tharan and Holiday, which were the only entertaining parts of the Consular story. I was EXTREMELY disappointed that I played a Twi'lek Female Sage and I could not have a relationship with the male Twi'lek, and instead I'm supposed to like this random soldier from Hoth. The Consular story literally holds your hand and has almost zero twists in it, and the few that it has, you already feel as if you saw them coming.
The Inquisitor suffers almost similarly, and you feel almost betrayed by the prologue. I played a Light Side Inquisitor, so this probably didn't help in any way, but I have been told that you REALLY need to play Dark Side Inquisitor to enjoy it, and I will vouch that Light Side just made no sense at all, so Dark Side probably couldn't make it worse. The prologue leads you to believe you have these certain character traits to overcome, but soon abandons the whole notion once you are off Korriban. There are a few twists in the story which help it some, but these redeeming points are few and far between. On top of all this, I feel as if EVERY companion save for Khem Val has absolutely no reason to be a part of your crew, and some that are on your crew make no sense at all from any motivational standpoint, like Ashara. Worst of all, and again this is probably because I played Light Side thus did it wrong, the ending was god awful from how I wanted my playthrough to conclude.
I am playing the Knight Story now... and I am halfway through Act 1, but at the moment, I can't see it being better than the #1 and #2 on my list, but it's definitely not as bad as the #6 and #7 on my list either.