I own a couple of Nooks but the Kindle DX is my first Kindle. Based on about a month of use, this is what I like and don't like about the Kindle:
Where Kindle DX is better than the Nook:
(1) The screen size rules: I can now read research papers (PDF) quite clearly.
(2) The user interface hardware buttons are very nice. I thought I'd prefer the Nook's swipe screen, but I was wrong. The Kindle's buttons & keypad are very convenient.
(3) The blackness of the device means that it pretty much disappears. I've found that I get immersed in a book quite quickly.
(4) The larger page size means that there are fewer page turns.
Where the Kindle DX could be better:
(1) I have never encountered corrupt epub books on the Nook in 3 years of reading (over 200 books). However, 3 of the 8 books I have read so far on the Kindle DX were corrupted. I had to delete them on the device and re-download them from Amazon. One of the books had the last three pages in a crossed out font because of some software glitch.
(2) Need way to annotate PDFs. I bought the Kindle DX so that I could read research papers. Not being able to add notes to these is silly.
(3) It would be nice to have page turn buttons on both sides of the Kindle. Having them on the right-hand side means that I can not read books holding the Kindle with my left hand (unless I were to turn the device upside down and learn to ignore the arrows on the buttons).
(4) The software user-interface is terrible. You need several clicks to just open up a browser. The browser is quite bad, so this does not matter much. But then, the Nook's browser is also quite bad; I can count on my fingers the number of times (in 3 years) that I have used the Nook's browser.
(5) Need way to see what music is loaded on the Kindle, to move to a specific song, to randomize the playlist, etc. Having only the option to play music in order is very limiting.
(6) Need way to set time interval before Kindle goes to sleep. I was trying to look at a paper and graph a formula (using my computer). The lKindle frustratingly kept going to sleep.
Ultimately, the corrupt books and the inability to annotate PDFs are huge problems. I hope Amazon plans to address these two issues in a software update soon ... the hardware is great, but the software for the Kindle DX is still quite raw and unfinished.