In general, I can never feel immersed by a third-person shooter. I prefer to 'look through my character's eyes', as it were. The only TPS games I've ever liked have been Gears, RE4, 007: Everything or Nothing, and now Dead Space, but those are some of the highest-quality examples of their genre there are.

Meanwhile, for FPS you've got Halo, Goldeneye, Battlefront (I play it in first-person, anyway), Call of Duty, Perfect Dark, Half-Life, and (to a lesser extent) Resistance, to name a few.

Both are mediorce as of late... I guess FPS is less mediorce though.

Third-person. First-person feels too limiting.

First person. It's more immersive.

Both

Well depends on what is the game about. Most FPS are about (spot enemy, shoot him, keep moving, repeat). When the character do something else than shooting, lets say melee combat, sword fighting or climbing walls I prefer third person shooters.
Example: Remember Jedi Knight Outcast? By default, it begins as a FPS. But in the way the player "almost need" to switch to third person view because his going to perform big jumps and later fight with the light saber.
Another example: Tomb Raider. (If Mirrors edge really works EA is going to prove me wrong). Anyway shooting doesn't play such a big role in Lara's adventures, but she can shoot alright.
Another example: RE4. Now, the resident evil series were not shooters until this one came up. But I have to admit that RE4 is a good shooter because it borrows a lot of things from FPS. When Leon Shoots the camera comes really close.

At the end, it may be just a matter of likes. With FPS, I feel like I am inside of a big spacesuit, with little control of the rest of my body (oh surprise, now I see why so many FPS's are space marines). From a third person perspective I can see "my" body so it gives me the feeling that I can use it and do a lot of things with it, apart from shooting.

3rd person, I like to know exactly where my character is plus fp can be quite claustrophobic. MP3 im lookin at you.
I felt more comfortable in 3rd person Metroid than 1st person so that would be my answer

TPS is better on consoles, FPS is better on PC. IMO.

I prefer TPSs, as I get some peripheral vision, but in faster paced games, I think FPS is better

I do like seeing my character on screen, and also I think it fits better with games that also include vehicles, so I dont think Halo 3 would have been a bad game to make into a TPS

For consoles I prefer 3rd Person