Though I'm a fan of both genres, I'd have to give it to 1st person shooters. Half of this opinion stems from my love of classic FPS games (such as DOOM). The other half is how the games play. It's somewhat hard to explain, but I've always enjoyed the feeling of staring down the barrel of a gun, as if I'm actually holding it. Normally, I don't actually care too much for immersion in games, but this feeling has always been mystifying. I've always felt great enjoyment in shooting down baddies with a perspective that makes it feels like I'm actually firing a gun.
I do love me some 3rd person shooters, such as Metal Arms, but as it stands, I enjoy an FPS just *that* much more.