My opinion is the Kindle Fire HD is more suited for people that fall into any of these categories: those who are new to tablets; those that are less technically inclined and want something easy to learn how to use; for people who already have a lot invested in Amazon’s digital content, especially movies; or for people who want to be able to connect to a TV.
The Google Nexus 7 is more suited for someone who likes more freedom for customization; for someone who wants a more open device with more overall software features; for those that want access to the larger selection of apps; for spec junkies who want the extra speed of the quad-core processor; or for those who have already owned an Android tablet or phone (if a person has already owned an open Android device, the Kindle Fire will likely feel to limited and closed-in).
The bottom line is this: both tablets offer something the other does not, and both are great values for the price compared to most everything else out there so you can’t really go wrong with either of them. The Kindle Fire is more limited from a software standpoint, but if you are willing to give up the warranty you can hack it to get access to Google Play for the same selection of apps as the Nexus 7.
Or, as I said before, Android Geeks will prefer the Nexus, iConsumers will prefer the iPad, and everyone else will buy a Fire.