If you are using your tablet as a media device: Kindle Fire HD.
If you are using your tablet as a portable computer: Nexus 7.
If you care at all about the underlying Android OS: Nexus 7.
If you are primarily buying this tablet for your family: Kindle Fire HD.
If you own a LOT of Amazon content: Kindle Fire HD.
I'd say bust out the pro/con chart for each device and decide that way. I know personally I would never be able to put up with the performance inadequacies that the original Kindle Fire had, and haven't seen any evidence that it was fixed in the HD.
My brother bought an original Kindle Fire, I tried it out and thought it's performance was horrible and I lost all interest in getting one.
The Kindle Fire HD performs completely differently and much much better, we have one and a Nexus 7. They both perform great, so well I would say that performance isn't a reason to choose one over the other.