I've had several friends and family ask recently whether they should buy Apple's iPad or the new Kindle Fire HD. The bottom line remains: the iPad still has the largest and highest quality app selection on the market for tablets. And apps are what make your device truly productive.
The most recent example was a music teacher asking me which would be a better choice. Hands down, the iPad. Garageband (an app for the iPad made by Apple) is one of the most powerful apps for any mobile device. The ability to record multi-track audio, synthesize instruments like full drum sets, orchestral strings and keyboards, USB mic and instrument support, and the ability to play music simultaneously with others make it any musician's dream.
In addition to Garageband, there are many apps for music students and professionals alike. Here are a list of apps I have found very useful:
And that's just a few. There are hundreds of apps that fall under these categories, and others such as teach yourself guitar, bass, piano, etc. Also, when reading digital sheet music, the bigger screen of the iPad as oppose to the Kindle Fire HD is much more useful.
If you're a jazz or big band player, you can even purchase multiple volumes of The Real Book on Amazon's Kindle app. If you've ever used a physical copy of The Real Book, you know how hard it can be to turn pages quickly or find the exact song you're looking for. Using the Kindle app on iPad, you can bookmark charts, make digital notes, zoom in on hard passages, and never carry around a deteriorating book again!
All that being said, there is one use case where I would suggest an Amazon Kindle. If your only desire is to read e-books and magazines, and nothing else, a Kindle HD or the new Kindle Paperwhite may be a better option. Chances are though, you'll want to surf the web, play with some apps and may even try to get work done, in which case the iPad is still the best choice.