I prefer the third person camera angle even though the majority of my favorite games are in first person. The third person camera gives a larger field of view and allows me to check my back sides, instead of having tunnel vision. I also appreciate the extra work by the developers making an extra model that lets me show off a character, pose them and understand them better. Some developers tend to like faceless cipher characters believing them to increase immersion, but I never have any doubts I'm playing a video game. I am not the Master Chief or Gordon Freeman. I am controlling them. Sometimes I'm a director guiding the avatar, sometimes I'm an actor playing a role. In this instance third person usually takes the player back to be bolder with characterization. This helps me, I would think Max Payne wouldn't shoot an unarmed man in the back, even if he is working for the bad guys and will alert me. Whereas I can also believe 47 will totally strangle the poor waiter so he can dress in his clothes to poison soup to a table. Third person games also usually have more varied combat and movement. It's weird fighting melee in first person and most of the time you are repeating animations and motions. When playing multiplayer on a FPS it really demonstrates how limited movement is. Everyone looks like they're shuffling while stuffed inside a refrigerator box [http://designreboot.blogspot.com/search/label/refrigerator%20box] while wearing a back brace.
So overall I see more, it looks prettier, I get to know the characters better, it encourages developers to be more creative with lead roles, it is better for varied combat and animations typically look better.