And, like most every other boy on the planet, I grew up with a knowledge of the Spider-Man mythos.
Simply put, The Amazing Spider-Man was very amazing.
The focus was not on Spider-Man, but rather on Peter Parker. You got to know the kid, understand who he was and why he became Spider-Man (not unlike the other 'new' Marvel movies). When you finally hear him call himself Spider-Man it's after he's actually become Spider-Man not just in costume but in drive. Uncle Ben also got more development (and Martin Sheen is a fantastic actor [and also President Bartlett]).
Further more, the relationship between Peter and Gwen is just, aw man, it just works.
Also: Emma Stone with blonde hair? <3
tl;dr: Josh really liked The Amazing Spider-Man and has so much love for Marc Webb.