The Marc Webb version simply had better actors. Andrew Garfield played a much better Peter Parker/Spider-man in everyway to Toby McGuire. Garfield was able to convey Peter Parker's social akwardness a lot better than McGuire. Also, Garfield is far more athletic than McGuire, allowing for some spectacular fight scenes in the Marc Webb version that the Sam Raimi version lacked to its detriment. Also, Martin Sheen made a superior Uncle Ben to Cliff Robertson, thanks most likely to his time as POTUS in The West Wing. Emma Stone made a far better love interest than Kirsten Dunst. Furthermore, Rhys Ifans played a better villain than William Dafoe, despite playing a B-list villain. And all of them had the right amount of chemistry.
However, that does not mean that the Marc Webb version was superior to the Sam Raimi version. Simply put, the Sam Raimi version had better pacing. It is a common failing amongst many Hollywood blockbusters that they need to rush through much of the story in order to get to the action that much sooner. This is not often the case. A proper film should take the time to allow the audience to digest what they had just seen, and allow the characters to develop and change based on the action taken. The Sam Raimi version did it the best. In contrast, the Marc Webb rushed into everything. Take for example, the second battle between the Lizard and Spider-man (Spoilers ahead).
Spider-man attempts to trap the Lizard in the sewers, mostly to get a photo of it to sell, a nod to Peter Parker's photographer career in the comics. He fails and almost drowns, and worst, the Lizard finds Peter's camera with a "Property of Peter Parker" sticker on it. In only twenty minutes, the Lizard decides to attack Peter's high school, allowing very little time for the audience to digest the fact that the Lizard now knows who Spider-man is. There are other exaples, but I don't feel like deconstructing them all.
All in all, The Amazing Spider-man is a film that I recommend to anyone who is antsy about The Dark Knight Rises coming out soon.
As always, Enjoy.