As someone who owns a first gen Kindle Fire, I would generally suggest someone to get the Nexus 7, and here is why:
Software Selection: You get a "pure" Android experience with the Nexus, which means you get access to everything in the Google Market (apps, books, magazines). You can even install the Amazon Market Place app (which is where you get your apps on a Kindle Fire). There are a lot of apps that are on Google but not Amazon, which is a big bummer.
Book/Magazine Selection: With the Nexus you can install the Kindle App (as well as the Nook app), so you can get eBooks from Amazon, B&N, and Google, as long as the correct app is installed (which are free). With the Fire you are stuck with buying stuff from Amazon (unless you go through the process of un-DRMing whatever you buy)
Interface: I really don't like the Carousel (sp?) interface of the Fire. Maybe it is because I am used to the Android/iOS interfaces by using them for so long, but I have seen other people complain. With the Nexus, you get the regular Android interface. Also, there are 3rd party launchers which can change the look and feel of the home screen, making things pretty customizable.
Upgrade Support: From what I can tell, my Fire is only a year old, and is not getting any more updates from Amazon due to them having new versions out. Google is generally pretty good about updating their Nexus line with new versions of Android.
Now, with all that being said, there are two reasons you might want to consider the Fire. The first is customer service, as someone else pointed out. I haven't had any issues with the Fire, but I have worked with Amazon CS in the past for other stuff, and they are generally very good, so I assume Kindle Fire support would be the same. Google isn't really known for their support (although I hear they are trying to fix that.
The second only applies if you have Amazon Prime. With Prime and a Kindle Fire, you get access to the Kindle Lending Library, where you can borrow one book at a time (from a limited selection; but it seems pretty decent), no more than one book per month. You also can watch the Amazon Prime Video selection from the Fire. I have Netflix (which both the Nexus and Fire have apps for), so this isn't a huge deal for me, because as of right now, Netflix has the better library. But something to consider.
I wouldn't consider the Nook line because I am already entrenched in both the Google and Amazon eco-systems
