The first one's songs are more mainstream, which is a plus for most people.
However, the co-op multiplayer is much better on Guitar Hero 2, with its system of one person being guitarist and the other being either bassist or rhythm guitarist. Also on the second each player can independently select difficulty level.
IMO for single player Guitar Hero 1 > Guitar Hero 2
if 2 "guitars" are available, Guitar Hero 2 > Guitar Hero 1