This might be too late, but I'd second the recommendation for the Nabi 2. It has the same processor as the Nexus 7, comes preloaded with a ton of educational software and books, and a very protective bumper. It depends, though, on how old your kids are. I think the Nabi is a great choice for 4-10-year olds, and even younger or older, but the company that makes it is about to start selling a couple of products on the other sides of that age range that might be more appropriate. The Nabi Jr. is targeted at 0-3, is even more rugged, but with a smaller (5") screen, and apps geared more for that age range, and the Nabi xD, which is a 10" tablet geared towards "teens and tweens" which will have less in the way of parental controls, more "social" features, and educational stuff for 6th grade and higher. Although Fuhu has said that you will be able to interchange the software so if you want to get the Nabi xD software for the Nabi 2, you'll be able to do that (or the Nabi Jr's).
In terms of how it compares, I don't know that much about the Nook or the Kindle Fire HD, but at least compared to the Nexus 7, the advantage of the Nabi 2 is that it is geared towards kids from the get go, includes its own case (very protective), includes a great deal of learning software and books (another saving point), has a microSD slot with the N7 lacks, and has a miniHDMI port, which the N7 lacks. The disadvantage over the N7 is that it has ICS vs. Jellybean (but it's so fast and responsive, that I hardly think this is a big deal! Plus it's very possible Fuhu might actually update it to JB sooner or later), the N7 has a better screen (better resolution and viewing angle), and the N7 has a GPS, gyroscope, and compass, which the Nabi 2 lacks. Oh, and the big one is that the N7 has access to Google Play, whereas the Nabi 2 doesn't. However, you can easily add Google Apps without rooting (Google Play still won't install or update apps though), and you can sideload apps from Google Play if you have another Android device that has access to it, although of course that's not nearly as convenient as having Google Play on the device itself...