GAE sandboxes you with their proprietary libraries, whereas AWS lets you write for unix/windows platform with minimal sandboxing. If you want to write a LAMP stack, you can just write a regular old LAMP stack with AWS. With GAE, you have to learn their java/python server libraries, then their blobstore/google cloud storage/googleQL, and so on.
Thanks for the breakdown. I haven't used t he service yet but I can see how that would be painful to deal with, especially if one wants to move their service in the future.