I admire Peter Parker a lot more than I admire Spider-Man.
As Bear pointed out, Peter Parker is an everyman.... I can
particularly relate to him. Always perceived as weak, geeky,
bullied at school, treated as an outcast, always doubting his own
abilities... somehow I see a lot of me in him. 
In contrast, I can't really relate to Spider-Man... I don't shoot
webs, crawl on walls, or have a Spider-Sense.