I've just came across this thread and I would like to say that many of my friends prefer The Amazing Spider-Man series and it some of the reasons why they prefer it really does frustrate me. I mean, I know everyone is entitled to their own opinion but some things they say like "It's more true to the comics." isn't really a reason to prefer it especially since half of my friends have never even read the comics.
I would like to say that, yes, I guess there are elements of the TASM series that do refer back to the comics more than Sam Raimi's trilogy, but is that really a reason to prefer it? In some cases, yes - but in most cases, no.
I love Sam Raimi's version for many reasons - the main one being Tobey Maguire. He was perfect as Peter Parker. That's not to say that I dislike Andrew Garfield, I just prefer Tobey Maguire because he's a more convincing Peter Parker. On the other hand, many people agree with that but then they say that Andrew Garfield is a better Spider-Man. I don't think either is a particularly better Spider-Man, they're different. Andrew's Spider-Man has more humour and whit whereas Tobey's Spider-Man is slightly less whitty but he stands by his responsibilities, in my opinion, a lot better than Andrew's Spider-Man did.
In Webb's TASM, Peter Parker was confident before he realised he was Spider-Man and before he actually used his powers for good. I think Raimi's Peter Parker was slightly less confident before he became Spider-Man, which I think was better.
Everything about Raimi's trilogy I prefered over Webb's series. In fact, my favourite marvel film ever is either Spider-Man or Spider-Man 3. I find this relatively surprising considering many people disliked Spider-Man 3 but I personally loved it.