Depends on what kind of games you play , competitive GPS like counter strike are great to have first person cuz you need more necessary elements to look than your character , first person tends to give more focus on aiming guns.
Third person is good for surrounding , aesthetic views . I play game like warframe and I like the third person perspective for this cuz I can look my nice character and also have more field of view to look what to shoot.
Different I think in both mode is field of view, when you plat third person it's more view than in first person but first person can be helpful to concentrate on critical situation.