Having played 5 toons to levels 14-20, I have to say that there is a huge difference in survivability between classes. My experiences only apply to those levels though. I do see a pattern though, and so far the easiest toon to play is my Jedi Sage, and the hardest one is my Jedi Shadow. Commando and Bountyhunter (healing spec, can't remember the name) are in the middle. Sentinel is extreme DPS and fun, but very squishy.
Also the final class quest for my Trooper on Ord Mantell was almost impossible to do with only solo quest experience, even though I did stop to grind some exp from mobs at a few points. There was a quest to use a computer console behind a few Pistolero signatures and adds that needed me to get killed on all of them killing the adds before dying to finally get to kill the signature. Until I dinged before the last one of them, which actually made the last fight easy.
So there definitely are huge differences between classes, and some of them (like my Jedi Shadow) actually become good only after a certain level (got a lot better at 20, should become very good at 25 or 26). Some seem to be very powerful right off the bat. Jedi Sage takes on elites with adds and at the end she and Qyzen are at full health. Shadow was almost dead in every single fight at the same point, using all CC:s and CD:s.
Some classes seem to get a LOT better later on, so it may take grinding through the levels to that point, or if one doesn't want to wait, rerolling to some "easier" class.