While the movie was a good take on the Spider-Man mythos, I wouldn't have said it saved or redeemed anything necessarily. I wouldn't even go as far as to say that The Amazing Spider-Man is a great improvement on Sam Raimi's Spider-Man trilogy (Spider-Man 3 not included). There are some things that each does better than the other. Therefore I wouldn't say either is better.
First off we have Tobey Maguire's portrayal versus Andrew Garfield's. Let me say that both actors are ridiculous. Each of their attempts at drama fall into the comedic on the regular. Specifically their ability to portray remorse. Maguire usually drifting into the realms of helpless screaming and demonic face distortions while Garfield blubbers like a clinically depressed chimpanzee.
One thing that TASM pulls off better than the previous trilogy is Spider-Man's sarcastic tendencies. The first trilogy only made Spider-Man crack jokes on the rare occasion and never really got into the extent of the character's cocky sarcastic persona. TASM doesn't delve that deep into that side of the character, however, the car jacking scene is a great example of the character's comic side, something they will hopefully expand on more in coming installments. Much like Maguire, Garfiled's awkward Peter Parker gets painful to watch. Does this make it ingenious acting? I can't decide.Garfield moved a lot more like a spider in this new film. He was able to pull off the contorted movements and poses associated with Spider-Man. I would go as far as to say that his body type was more what I would expect Spider-Man to look like over Maguire's. Garfield is ungodly thin and his that look of an athletic contortionist where Maguire was pretty built and looked more fitting as a superhero. While that may seem desirable in a superhero move, I feel as though the leaner look is better for Spider-Man who often relies more on speed and strategy than brute strength (it isn't The Hulk or Superman afterall).
One thing I didn't like about TASM was the use of CGI. I thought the computer graphics in this movie were horrible. If you look at the difference, the original trilogy didn't seem to use too many computer generated special effects, only where they needed it. Since the villains were human, they could do a lot of real stunts. When they DID need CGI, like in the case of webslinging and the creation of the symbiote in the third movie, it looked great. Unfortunately for TASM, the primary antagonist was required to be CGI, he looked pretty terrible. This also made the fight scenes CGI and I personally prefer it when actual actors are actually doing things. This leads me to The Lizard, not the greatest villain to have chosen in my opinion. Also Rhys Ifans doesn't do the best job, he makes for a very bland character, there's little character development on the part of The Lizard also. They decided to include a scene where The Lizard persona is talking to Dr Connors, much like Norman Osborn in the first film. However, Ifans can not pull it off as well as Willem Defoe did. On top of that, they introduced a man that will supposedly be The Green Goblin in the next installment. This actor is basically acting like Defoe's Norman Osborn. I will be interested to see how they do The Green Goblin, especially since they caught some flack for putting him in armor last time.
Another thing is that the previous trilogy followed the comics better in a lot of ways, even though TASM gets a ton of points for having web shooters instead of organic webbing. It also doesn't kill off Uncle Ben's murderer. We'll have to see if it follows the story of Peter's parents in the coming sequels, I honestly feel as though it won't. Overall, The Amazing Spider-Man is a decent, yet flawed, adaptation. I wouldn't say it's any better or worse that the first Spider-Man movie, but it is deserving of the title of Spider-Man.
