Andrew Garfield is a much more convincing and realistic Spider-man. He has a real natural feel to him as Spider-man and as Peter Parker. Spider-man is a smart, witty, know-it-all, pulling out jokes in the middle of battle. Andrew Garfield is best at doing so and pulls the one-liners off with such ease.
Yes spider-man is meant to be serious but it also has a humorous side. Peter Parker is a wise cracking high schooler he can't take every battle serious, he needs to lighten it up or perhaps he would panic. Andrew Garfield does a tremendous job presenting that. I am still a fan of the Raimi trilogy, 2 is still perhaps my favorite of the 3, but Garfield has a much more realistic personality than Maguire did.
I don't believe the reboot was childish at all, the relationships between Gwen and Peter are quite believable especially by the performance by Andrew Garfield. Not only that but Tobey didn't come off as a genius, but more of a lonely geek, and an odd one at that. Garfield truly seemed like a smart and important figure.