The Amazing Spider-Man brought free-roam back to the light and the game also added a greater fighting mechanic. It kind of felt like I was going back to Spider-Man 2 for the original Xbox with the simple fact that anything could happen. You could be enjoying a nice web-swing through Central Park until a sudden spidey sense kicks in and you're off to save the day. The game also held secret Spider symbols to unlock certain Spider-Man suits. Some you had to get at a certain date which you could easily switch your console's date to in order to get the suit and no penalty would be at your mercy.
The suits didn't disappear or anything! I personally used the black Symbiote suit from Sam Raimi's Spider-Man even though Spider-Man 3 was a flop. I currently await the arrival of The Amazing Spider-Man 2.