So I've had my Fire for about a week, last night I got a chance to play with a nook tablet. It was rooted, installed GO launcher and bunch of other apps. Here are some things I found out besides the HW specs differences.
1) Fire is much smoother. Hardware-wise, the surface of Fire is glass, while Nook's "feels like" plastic. Your finger can definitely feel the difference the moment you touch them. Software-wise, the browser on Fire scrolls better, esp. on some lengthy websites. (That's all done after it stopped loading, so Silk is not the reason.)
2) While nook has one more button than Fire's zero, Fire has three software button always there. Some apps like to use the back button as exit, which can be annoying on nook since you have to manually kill them in the launcher or nook home.
3) Nook has better compatibility with Android apps. On Fire, there is one video player crashes whenever I bring out the on-screen control. On Nook, it works just fine.
4) Pdf file shows better on Fire. I have a photography book (PDF) with some beautiful pictures. When viewed on nook, some of the color washed out, like on a 32k color screen. I tried different pdf reader ( build-in, adobe reader and one I can't remember, they are all the same. ) I don't think it's a hardware problem though, since JPEG pictures are almost identical on both devices, apart with a slightly different tint.