No matter what new material Amazing Spider-Man brings to the table, there are certain elements from director Sam Raimi's first Spider-Man movie (Peter Parker getting bitten, Uncle Ben's demise, etc.) that have to be recycled here - unless Sony really wants to divide the fanbase, more than TASM's rumored altered origin storyline already has.
TASM incorporates plot elements from the "Ultimate Spider-Man" comic book continuity - including, the backstory about Pete's biological parents - and constricts the timeline to Spidey's high school years, rather than cover his high school experience and starting out in the real world (a la Raimi's film).
The final result looks to be a Spider-Man flick that deeply explores how a teen - already wrought with identity issues and the ordinary pangs of adolescence, would really handle the responsibility of being a superhero (something I feel we have not seen before).