I'd recommend the Nexus 7, if only because it will receive Android OS updates as soon as they're available. With the Kindle Fire HD, you're at the mercy of Amazon as to when you'll get updates for your device.
The decision for most people largely depends on which digital marketplace they've already purchased more digital goods from: Amazon or Google Play. If you've already dropped a good chunk of change on Kindle e-books or Amazon MP3s, that would give the Kindle Fire HD the advantage. If you haven't purchased any digital goods from either the Amazon or Google Play stores and don't intend to, again, I'd say the advantage goes to the Nexus 7.
If you're still unsure, you might try a quick "kindle fire hd vs. nexus 7" search on Google as it turns up several relevant articles.
But for those who want a tablet device specifically for reading, I agree with Atown's recommendation of the Paperwhite. Digital ink is much easier on the eyes (well, at least my eyes) than a tablet screen, especially over prolonged periods of time. I'll probably pick up a Paperwhite 3G at some point and wait for some company to produce a reasonably priced 10" tablet with a pressure sensitive stylus, preferably a Nexus device with pure Android (with none of that Touchwiz shenanigans).
EDIT: Oh, and if you have Amazon Prime, that's a point in favor of the Kindle Fire HD as you'll be able to access Amazon Instant Video. I've read that it may be possible to get AIV working on the Nexus 7, but it sounds like you'll have to jump through hoops to do it.