I want to preface this by saying that I have been both an Amazon and B&N customer for many years (physical book purchases up the wazoo!). I have not purchased a Nook, but I have used one many times as I have a few coworkers who purchased them. I will try to be fair about the pros and cons of both. Also, I work in the tech industry, so my experience with a rooted Nook may not be one that most users of these forums can speak to if all they've done is played with a demo model in the B&N b&m stores. It's a different experience, but one that is really only available to people who don't mind hacking the device. Last, this all just my opinion....I'm not here to try and sell any of this as "fact." Take it all with a grain of salt......
Pro Kindle: I loved my Kindle 1st Gen, and I adore my Kindle 2i. I'm a tech gadget geek, but without a doubt the one I use most often is my K2i. Amazon customer service has been nothing but amazing for me, which includes a broken K1 that they replaced for free after I had the device for over 10 months. It's a light device that does what I want it to do very well. I am a voracious reader, and the near 2 weeks of battery life I get (with wireless turned off) is - simply put - awesome. The site design on Amazon is much better than that of B&N (easier navigation - better search, wishlists, recommendations based on purchases, etc.). I also often find that ebooks are cheaper on Amazon when compared to B&N. I like the number of accessories available for the Kindle (the cover choice is astonishing at times). I love the Kindle and Amazon as I've had nothing but positive experiences with both the device and the company.
Negative Kindle: The release of the firmware updates is not as timely as it should be. B&N had a Nook update within the first month of release based on the negative feedback users had about the navigation and speed of the device. Amazon provides worthwhile updates, but they are sloooooow to incorporate the suggestions of their customers (example - folders/categorization has been requested ad nauseam since the Kindle 1 release....we're just getting it - kind of? - with the 2.5 update). On the other hand, the Nook has had a few updates, almost all of which were direct responses to customer criticisms and requests. Amazon has also promised an app store for the Kindle, but no one knows when/if this will ever be available, or how it will work with just an eink display.
Pro Nook: The Nook's android OS was hacked in the first 48 hours of release, which allows for independent development of hacks, apps, and changes to how the device functions. Admittedly, one needs to be tech savvy to work with this, but having had personal experience with a rooted Nook.....it's awesome. Most companies would work to ban or block this kind of modification immediately, but B&N seems to be taking a slightly different approach. The user community is doing some amazing stuff that is actually influencing what B&N is doing to improve the Nook....they are using these hacks to see just what their customers actually want...and then they are developing their own solutions. The LCD screen is going to allow for greater app or addon development simply because of its responsiveness compared to the eink display. The ability to take a Nook into a brick&mortar store to get exclusive previews and content is pretty darned cool and makes me wish that Amazon had a physical presence other than it's warehouses wherein only the Amazon oompaloompas are allowed to roam.
Negative Nook: At least 2 of my friends have cracked arrow buttons already. That kind of build failure is poor, and shouldn't be tolerated. It's a bit heavier and thicker than the Kindle, which does add up if you read for hours (like I do). The battery life is shorter, but is only an issue if you can't charge it at least once a week. Initial software issues made the Nook receive a lot of negative press, but the firmware updates have supposedly resolved a lot of the issues. I'm not a fan of the B&N website store as it seems clunky and slow to me.
The bottom line, however, is that both devices are amazing pieces of technological artistry and you can get books for both from multiple sources. If you are unfamiliar with how to convert books for your chosen device, check out the Calibre forum here on mobilereads (it's AMAZING). It will allow you to get books from many sources and easily manage, convert, and upload to your device with just a few button clicks.
Both devices are great and both excel at reading (I'm not a big fan of the mutli-purpose internet tablet/mp3 player/video machines that some love.....I want an ebook reader that lets me read comfortably for long periods of time - both the Kindle and Nook do this very well).
I will say this, however.....As much as I love my Kindle, if the B&N Nook continues along the path it's on, I will be eager to see what the next hardware rendition looks like. It's a great design that just needs a few tweaks to improve build quality and responsiveness.....but I can't fault them for a few stumbles when the K1 had its own to recover from (just think giant buttons that send you flying through page turns each time you pick up the device). I also look forward to seeing what Amazon releases next, but worry that B&N beat them to the LCD navigation (and the resolution of bugs and fixes that it required). I worry that Amazon may release a new touchscreen device that will need to go through its own growing pains.
It's probably plain to see that I think both devices are excellent, and that you can't really make a "wrong" choice. I wouldn't trade my K2i today, and neither would my friends with Nooks. If you pick one and use it long enough, you'll find the reasons you love it.
I hope that helps and that I didn't ramble too much. Good luck with your decision!