I'm a little biased, because I've got an old Kindle Fire and a new Nexus 7, but when you put the two of them side by side, I'm still going with the Nexus 7. It's not the hardware, because the Kindle has an edge there. It's the Android. I would just rather run a device that isn't dependent on a single media company. That said, I'm positive that anybody getting either of those devices is going to love them.
I'm also a little disappointed that Apple hasn't released a seven inch iPad model yet.