My Answer: OK, I go back and forth with this one. I have owned or worked with different versions of both Nooks and Kindles. I have had good experiences with both.
My very first experience with ereaders was with the Kindle DX that was purchased to work with my students. They were fun, but for me, I thought they were too large.
I then purchased the first generation Nook. I loved it, but made one big mistake when purchasing it, I had not bought the warranty. What I did not know that with all the first generation ereaders with e-ink, they often messed up. And, because I had not purchased the warranty, when mine messed up - I was left without!!! The companies do not "fix" the devices, they only replace them. I learned the next time around.
The Nook is not the only device with e-ink issues. We have since purchased some basic Kindles for school, and they too have messed up. We have had to have several of them replaced. Ugh! Yes, Amazon is wonderful with dealing with the issue, and quick to replace, but it is a pain in the ........!!
Now, my youngest daughter has a Kindle, and it has yet to mess up. I do think she is more careful with it than some of the students are though. So, if you are careful, the e-ink issue might not be an issue at all!!!!!
I have purchased the Nook Color when it came out, and I fell in love! It is a great device! I have even dropped it, and it still works. No issues with the e-ink, as it doesn't have it!!! I think the tablet devices are the way to go.
I have not personally had experience with the Kindle Fire or the Nook Tablet, but I have heard many rave reviews for both. I don't think a person could go wrong with either one!!!
Right now, I am personally using an iPad with apps for both the Nook and Kindle - among many other ereader apps. I like having them all in one. They both have great free books available for them, so you don't miss out on much. Even if you only read the free books, you have so much to pick from.
One benefit that I see with the Kindle app (or devices) that I have not seen with the Nook yet - and it may be that I just haven't happened on it yet - the ability to email documents to your device. As a book reviewer, you receive many books that are PDFs. The email option is wonderful for this. Also, NetGalley uses this option to send your books to your Kindle as well.