While Amazon's tablets run the company's Fire OS, a skinned version of Android, you can't get access to the Google Play store unless you hack the tablet. In contrast, Barnes & Noble's Nook Tablet 7 give you access to the Google Play store out of the box, a selling point.
In many other respects the tablets are very similar -- at least from a specs standpoint (for all we know both tablets could be made in the same factory in China). They're both 7-inch tablets, their resolutions are the same at 1,024x600 with the same pixel density (171 ppi), they have basic front and rear cameras and both come with 8GB of built-in storage but have expansion slots to add more (microSD memory cards up to 128GB). Barnes & Noble's tablet does weigh a couple of ounces lighter, however.
I haven't gotten my hands on a review sample yet, but I'll be able to give you a better performance comparison once I do. The Nook Tablet 7 is available for preorder now and is available in stores on November 25.
Here are its key specs, according to Barnes & Noble: