What are the differences between the Spider-Man and Amazing Spider-Man universes?

Sam Raimi's Spider-Man trilogy was rebooted when Sony released Amazing Spider-Man, and part of this reboot were changes in the in universe story and world. Peter starts dating Gwen Stacy instead of Mary Jane, for example. What are the differences between the two universes?

I'm not looking for a scene-by-scene nit picky rundown here, but rather the larger, broad-stroke differences between the two settings/stories.

Best Answer

Here's a quick rundown of the changes so far.

Spider-Man

In Sam Raimi's Spider-Man, the web shooters are organic mutations that were a result of the genetically engineered spider bite.
In Amazing Spider-Man, they stuck to the comic book roots and had Peter invent mechanical web shooters that use a formula partly developed by his father.

Peter's Past History

In Sam Raimi's Spider-Man, Peter's parents are dead but we have no other information on them.
In Amazing Spider-Man, Peter's parents death was part of a conspiracy concotted by OsCorp.

The Osborns

In Sam Raimi's Spider-Man, Norman Osborn wears a mechanical suit to become the Green Goblin.
In Amazing Spider-Man, Harry Osborn is biologically transformed into the Green Goblin.

Peter's Love Life

In Sam Raimi's Spider-Man, Peter's first girlfriend is Mary Jane Watson. Gwen Stacy appears later on to complicate matters a bit but MJ remains his primary love interest.
In Amazing Spider-Man, they once again stayed loyal to the comics and had Gwen Stacy be Peter's first love. Mary Jane was slated to appear in a minor role, but she was ultimately cut. Spidey's off/on lover from the comics Felicia Hardy makes an appearance as well.

Misc

In Sam Raimi's Spider-Man, the Daily Bugle and it's publisher J Jonah Jameson are featured heavily.
In Amazing Spider-Man, the Daily Bugle starts to appear in the second movie but Jameson has not made an appearance yet, although he is mentioned.