Neither the Nook Tablet nor the Kindle Fire handles most forms of multitasking adequately. Sure, you can play music in the background while you read. But when you move from one app to another, these tablets tend to close out the app, rather than suspending it. As a result, when you return to an app that you recently left, you may not go back to the spot where you were last (both the Nook Tablet and the Kindle Fire have email clients forget where you were).
Neither tablet makes it clear to users whether they're capable of true multitasking in the background. And neither handles switching among open apps very well. On the Nook Tablet, a few apps appear in the bottom status display (including Pandora, the native music player), but their behavior is by no means consistent.
To sum up, both tablets are significantly inferior to the iPad and to other Android tablets in their multitasking capabilities.
Winner: Nook Tablet
With Android devices, you can choose the apps, shortcuts, and widgets that you want on your home screens. But both the Kindle Fire and the Nook Tablet have custom interfaces built on top of Android 2.3, and those custom interfaces give you far less freedom to tweak them.
Still, the Nook Tablet offers many more personalization options than the Kindle Fire does. For starters, you can add your own image as wallpaper to any of the three home screens. You can also move favorite books, periodicals, or apps to sit anywhere on one of the home screens--including layering icons on top of one another. A scrollable carousel of recently accessed or received books, periodicals, and apps runs along the bottom of the screen. If you don't want something to appear there, you can just delete it.
The Nook Tablet also provides more options for displaying your content in its libraries. Most notably, under the 'Library', a 'My Stuff' tab leads to your own bookshelves (basically, content collections that span your apps, books, magazines, and newspapers). From My Stuff, you can peruse your files through a decidedly non-Android-like file viewer, see what's archived online, and view the books that you can lend.
Amazon's Kindle Fire has a cleaner-looking home screen, but it's fairly locked down. You can't select a lock screen image or a background wallpaper of your own, and you have no control over what appears in the central carousel, which covers everything from books and periodicals to music and movies to apps and Web pages--and you can't delete any of them. You can add four apps to a Favorites shelf at the bottom of the display, and you can add multiple shelves. Oddly, you swipe down to find more "pinned" Favorites. I did like being able to drag favorite icons around to reorder them on the Favorites shelves.
Next: Buying or Renting Books, Music, and Video; Music Player; Speakers; and Email