I have a Nexus 7, and the wife, to show me how much smarter she is, bought a Kindle Fire HD 8.9 a month ago.
IMHO the Nexus is far and away a better device. Kindles are pretty locked in to Amazon, and they do their best to exclude anything Googleish. (Of course, Google makes it tough to use Amazon in the Nexus, but I digress.) The Kindle's Android system is significantly downgraded. The default browser is poor. However, Firefox can be loaded onto both devices. There is a much wider range of usable apps for almost any purpose on Google Play as compared to Amazon.
Looking at the specs for the 2013 Nexus, it seems to me only a moderate upgrade. No reason to toss a 2012 in favor of a newer one.
However, I much prefer my desktop to either tablet for normal daily computerizing.