Hm... really a hard question.
I played all Imperial Classes and now JK and Trooper to 50 and at some point I enjoyed all of them, let me get into detail a bit:
1) Sith Warrior
+ Story: I am a big fan of political stories and Darth Baras is the best mind in the Empire, more would be a spoiler but the entire first act was a great combination of politics and character development, also the biggest impact of Light/Dark-choices I encountered
+ Playstyle: (Annihilation-Marauder) Takes time to get used to, but once you have a working rotation the combination of DoT and self-healing is just fun. The Rage system is not very forgiving though, use up to much Rage you will only hit with normal attacks for some time.
+ Companions: Except for the Talz, everyone of them has his own character and a lot great dialoge. Vette and Quinn are especially great
= If you want to play a Sith, take a Warrior
2) Sith Inquisitor
- Story: First Chapter was pretty boring, there were only some good parts, like the plot on Nar Shadaa. You mostly end up doing the same thing 4 times. Chapter 2 is not much different. 3 is a bit better, but still not halve as good as most other class stories. I expected politics here as we are supposed to be the "intelligent" Sith, the master of manipulation that Sidious was, did not see that
+ Playstyle: Played both an Assassin and a Sorc for some time. Both play just awesome. I liked the Sorc a bit more as the mixing of Force and Melee is not so much what I like (mostly visually). Shooting Lightning out of your fingertips is just pure fun, especiall with the Madness tree, that allows for infinite Force Lightning.
- Companions: Especially in the area of romances your companions fail, badly. As female you may choose from a pirate with a bad attitude (which is so over the top that it is ridiculous) or a pirate with a bad attitude, as male you get Ahsoka Tano's ancestor with the same annoying character. In the non-romance section we have a monster that would eat you, if it could, a crazy archeologist and a terribly sucking up Apprentice (who really is only interesting in the first scenes where you meet him)
= Play the class for the Playstyle and you will have fun, play it for anything else and you won't
3) Bounty Hunter
+/- Story: You want to play a Bounty Hunter, you will play a Bounty Hunter, your story resolves around heads with price tags. If you like that, good. A change happens after the climax of chapter 2 and I liked that a lot. The end was really enjoyable and is also very interesting to fill in some blanks when you play a Republic char.
+ Playstyle: (Dps-Merc): It is fun, but can get a bit dull compared to other styles. You pretty much punch the same 5-6 buttons again and again, maybe a cooldown inbetween. That is both good (as it is muuuuch easier to manage then a SW/JK which is pretty much like playing a piano) and bad (as it gets stale to only shoot rockets into faces)
+ Companions: Mako is great both characteristically and gameplay-wise, Gault is the good and funny version of the guy with the bad attitude, Blizz is... just Blizz, fun and cute, and then there is Skadge. I think I will never forgive Bioware for not letting me shoot the guy... for a lightsided BH taking him onboard is like complete brainwashing with hydrocloric acid. The one and only companion that I never gave any gift and have at - 50 Affection or so....
= If you like a simple and straightforward playstyle and can live with being a bounty hunter for most of the story, its surely fun.
4) Imperial Agent
++ Story: Next to the SW and the JK, this is the best story in the game. Can't say much more about it without spoilers but you really get a lot of suprises, also having Jo Wyatt as voice actor made me never touch a male agent, too great to hear her talk.
+ Playstyle: Did both a healing Operative and DoT-Sniper, loved the visuals on the Heal-skills, very powerful and very nicely thought out. The DoT Sniper has some problems, f.e. that I could never decide if I should use cover or not (problem with a shared tree I guess) and that the feeling of really being a sniper did not come up. Probably with the Marksman tree that would have been different.
+ Companions: Many people dislike Kaliyo, I did not. She is pretty much Jack from ME2 (and I mean more then that they share voice actors and a fondness for tatoos and bald heads). I found her very well fitting for the agent, leaving her to attract attention while I quietly snuck in the enemies back (not just in combat), also her chaotic lifestyle is fun to behold. Vector was also not that bad, a bit crazy, but whatever. Actually I liked them all, they were very great to have around.
= Likely the best Class to play for fun. One hears that endgame damage is lacking, but one hears a lot of things.
5) Jedi Knight
++ Story: Very diverse missions and the end of Chapter 2 just blew me away, even though I knew what was coming. Awesome.
+ Playstyle (Guardian-Tank): Tanking was a new thing for me, so it took me a while to learn about it. The number of skills really are a lot to manage when you come to an MMO fresh, but it builds up slowly so you can get used to it on the way to 50. It definately is fun, though very unforgiving
+ Companions: From the first to the last these guys are simply great. Enough said.
= Definately fun and likely the class with the most impact of overall story.
+ Story: I read many people disliking the story, I can't see why. From the start on Ord Mantell its awesome to see the developments. You also gat a very strong connection to the powers that be (the senate) and General Garza is likely the best (and strictest) COs in galactic history. Also in Chapter 3 I encountered possibly the greatest and hardest decision in the whole game. Awesome. Also you notice very soon that Bioware did a lot of military plots in ME1-3 and implemented some of that, not to mention Jenniffer Hale, what else could one want?
+ Playstyle: (Shield Specialist Vanguard): After tasting Tanking on the JK, I got addicted and did it here too. Only reached 50 a few days ago, but I like what I see. Ranged tanking is very nice but you also see a big difference with the Guardian tanking. At the moment I prefer the Vanguard.
+/- Companions: Well, there are some I really liked, like Elara and Forex, the others are a good medium. I did like the idea of actually being a strike team though, that was fun.
= Definately better then what people say about it, very funny and with Jennifer Hale as voice actor a slight ME-feeling was there.
Phew... that got a long post, hope it is informative.