play both. Coz other than shape and the word "guitar". Both have absolutely nothing in common thats worth thinking to decided which one to play!
guitar hero doesnt help in making/writing new music
real guitar doesnt help in making owner in the house in front of tv set looking like real rockstar
guitar hero doesnt train any actual skill in real guitar playing other than perhaps better cordination between brain and hand movement
real guitar doesnt make you sound that good coz if no backing track, real guitarer is as dead as the boring dude who find entertainment looking into blank space
guitar hero is digital , 1, o, 1, 1, 0, 1, 0, 0
real guitar is warm, like how guitarer like to describe effect, warm delay, warm overdrive, and my favourite term, by them, warm chorus.