Entertainment Weekly has an interactive feature up detailing the changes in Spidey's suit for The Amazing Spider-Man 2. Most of the changes are visual, but at least one is purely for Peter Parker's enjoyment—a built-in MP3 player.
Costume design Deborah Lynn Scott explains Spidey's musical webshooter controls:
We wanted ours to have an MP3 player in it. You'll see early on in the film that he can turn music on that he's listening to inside the costume through his web shooter.
Many of the other design changes are meant to return the Spider-Man suit to a more classic look. The image up top is a crop from the feature image. Head over to EW and click on the plus signs to read more about the changes to the eyes, chest logo, and more.
'Amazing Spider-Man 2': 'The Suit Is Improved' [Entertainment Weekly]