Playing first person shooter on a mobile phone sounds like literally the worst possible experience. You need physical controls for accuracy touch screens are terrible for that plus of course you're obscuring a good chunk of the screen with your fingers.

There are a few good mobile games, although I admit not many, but the good ones work with the limitations of the medium rather than trying to simply brute force through them. Good ones include things like Hitman Go, Threes, And a fairly possible Eve Online mobile game, which was only really let down by being Eve Online.