The controls of Godfather really push it over the top. Graphically GTA is better. GTA also has over the top themes going on. The shooting and fighting mechanics on Godfather blow away GTA's by far.
I love both. I prefer the controls of the Godfather and I liked the RPG-style character building and the business takeover stuff. But I still like to play GTA to drive around in outrageous vehicles listening to old-school music and laughing at the crazy commercials (like Exploder: Evacuator Part 2 in Vice City)
Godfather definately will keep you playing for a long, long time.