It depends on the game itself, really. There are FP games that I like a lot (like Left 4 Dead and Fallout 3), and TP games that I like a lot (Dead Space, Batman: Arkham Asylum).
There ARE some exceptions though. Like, playing Fallout 3 in third person is really annoying, the camera is too far away from the character and you can't properly see what's in front of you. It's also hard to pick up small items with the camera being too far away. The only time when the TP view comes in handy is when you want to see enemies hiding behind walls or rocks.
The idea of playing Mirror's Edge in TP is another example. The thing that makes that game so fun and unique is the movements in the camera while running, jumping, etc. The amount of realism, I mean. Playing that game in TP view wouldn't even be half as satisfying in my opinion.