Naturally I was sceptical about them starting from scratch only 10 years after the Sam Raimi franchise started, but I think that benefits The Amazing Spider-Man. Without the 2002 version they likely would've spent considerably more time setting up how he became Spider-Man. As it is they seem to get through that part of the story briskly which would be more noticeable and frustrating if they haven't covered it in another film years before. But works in a way because having seen his origin already you really want to get past it and move on to crime fighting and lizard bashing.
I probably wouldn't have plumped for such an imposing villain for the first film of a re-boot, but it's still one of the best origin stories I've seen.