Interface: Nook is a touch interface with buttons for certain actions (home screen, flipping pages). Kindle WiFi is purely a button interface (the Kindle Paperwhite does have a touch interface, but it costs more than $100). Nook also has a microSD card slot for expanded storage space, while Kindle uses Amazon Cloud storage to expand its storage space.
Software Features: Nook has slightly better page-turning algorithms on eInk screens than Kindle. To get an ad-free experience is $79 for Nook and $89 for Kindle (you can get the Kindle for $69 with ads). Nook is also based on Android, so it is a bit easier to root than the customized Linux software that the eInk Kindles use. Both vendors also have apps for use on other devices, such as your smartphone or PC, so you aren't limited to reading books just on the eReader.
Free Book Features: Both eReaders are supported by Overdrive, which is the software most public libraries use for lending ebooks. Both vendors have free book sections of their website and rotating book discounts that might include free books on certain days. Kindle has some additional free book features for Amazon Prime members. Nook allows free reading of any book (regardless of price) for one hour a day at a physical Barnes and Noble store. The Nook directly supports the EPUB format for books downloaded from Google Books, Open Library, Project Gutenberg, etc. The Kindle does not support EPUB, but there are free software programs like Calibre to convert from EPUB to formats that Kindle does support. Some free book sites also provide books in both EPUB and Kindle formats.
Vendor: You have Barnes and Noble for Nook and Amazon for Kindle. Both vendors have about the same price for paid ebooks, varying by a few pennies here and there (barring any sales they might be running). You do have to have some concerns about the lifetime of the vendors, since your paid ebooks aren't really "yours" as a physical book would be. There could be loss of access to content you paid for if the vendor were to go belly up (or were to remove that content, which did happen in the past with Amazon). However, the Nook is still useable for future book purchases/reading, even if Barnes and Noble were to go away tomorrow, since it can be rooted to stock Android, which means you could just install the Kindle app on it.
Source:
http://www.bogleheads.org/forum/viewtopic.php?f=11&t=120861&p=1767405