Kindle does allow books from outside Amazon, they have to be DRM free and in the mobi format. If the books are DRM free, you can easily convert them using calibre, which is a great program to organize and maintain your digital library.
I am not familiar with the nook, so I can't give you any help there. But I do believe it supports library books. If that is something you are interested in, that may be one of your deciding factors as the Kindle does not.