My wife and I did a lot of research before we bought Kindles for each other. What we discovered in our research is that the Kindle is generally considered a superior device overall, has a superior user-interface, and its battery lasts longer. The Nook's only significant advantage is its library lending feature (something which the Kindle may add at a later date, anyway). Since we've bought about 100 paperbacks over the last several years and have not borrowed a single library book (we would never want to have to wait for a book we want to read, or accept whatever book happens to be available at the time), the library lending feature of the Nook didn't hold any promise for us, so our decision was easy.
It should be noted that you actually have three main choices: Kindle, Nook and Nook Color - the Nook Color is so different in technology from the Nook that it must be considered a separate device. And specifically not recommended, as far as I'm concerned. Although I recommend the Kindle, you really cannot go wrong by selecting the (regular) Nook instead. It is almost as good as the Kindle, and once you have it, you can readily convince yourself that it is the better device - they are apparently that similar in quality. The Nook Color, on the other hand, is different. It is backlit, and that's simply a bad idea for reading. It is very clear that e-ink (the display technology for the Kindle and the regular Nook) causes far less eyestrain than a backlit screen.