I like playing in both PoVs. First-person allows you to BE the main character, to BE in the heat of the action. Helps give a sense of realism to a video game, even if only a small one. Third-person just lets you view the character you're playing as, which can break immersion in a lot of instances for me.
In reference to my earlier comment, I actually realized that technically Undertale is a second person game. Spoiler: Undertale spoilers Since it's actually narrated by the first fallen human, not the character you play as. It's that character's perspective of what your character does. I think it's really clever although I don't know if any other game could pull it off.