I personally prefer Rock Band 1 and 2 over Guitar Hero. If you're willing to spend money then Rock Band is the way to go with sooo much DLC to purchase. The game is also very clean looking and plays great on big tv/audio setups. The fretboard being black (and improved in RB2) makes gameplay feel so much less cluttered than Guitar Hero.
Plus Rock Band is made by the creators of Guitar Hero 1, 2, and 80s.
I wouldn't say Guitar Hero has a bigger fan-base, and if it does it's mostly just because of the name Guitar Hero. Which Harmonix built in the first place. If you don't like a sellout company, and love extra content, then go for Rock Band.
However, if you just like the look, feel, etc of Guitar Hero, well, go with Guitar Hero. You can always rent one or the other to see which one you like.