I went back and forth between the Nexus 7 and Kindle Fire HD. I love the Nexus 7, but I love the Fire HD just a bit more.
Reasons I went with the Fire HD.
* Better looking screen. The Nexus 7 colors are a bit washed out, the Fire HD has much better colors and white saturation.
* Much much better sound. The mono speaker on the Nexus 7 is pretty weak, when listening to podcasts or dialog on some video's it's even hard to hear people are saying. The Fire HD by contrast has two speakers, each with dual drivers, much louder and clearer. And the stereo sound is nice for watching movies.
* Kindle Lending Library. This is exclusive to Kindle hardware. You can borrow one ebook a month, keep it as long as you want, over 100,000 books available, no waiting. Requires an annual $80 Amazon Prime subscription, but anyone buying a Fire HD really should get Amazon Prime.
* Kindle OS. In a weird way the Kindle OS is a good thing on this tablet if you are into Amazon content, ebooks, videos. I love the recommendations and how easy it is to find and buy new content.
I've rooted my Kindle Fire HD, have Google Play and other Google apps running smoothly. Using the Apex launcher as my home screen. Some geekiness is required to set this up, but it wasn't too difficult. And after the tinkering this feels like a real tablet now and I don't feel locked into Amazon's content.
Dolphin or Chrome definitely needs to be installed on the Fire HD, because the stock browser is the most miserable web browsing experience ever (probably even worse than Nook's browser). But real browsers perform great on this.
Nexus 7 is definitely faster, and I think the Nexus 7 feels better and more comfortable in the hand. But overall, and as an Amazon Prime subscriber, I like the Fire HD a bit more. It's close though, I don't think you could go wrong either way.