I don’t have a Kindle. I’m only familiar with the iPad. So I cannot confirm or deny Manualman’s issues.
How much they hold is a matter of storage space. The current generation iPad comes in 16 GB, 32 GB, and 64 GB. The current generation 7" Kindle Fire HD only comes in 16 and 32 GB. The current generation 8.9" Kindle Fire HD comes in 16, 32, and 64 GB, however the 64 GB size is only available with the 4G data plan (which I wouldn’t recommend unless you travel a lot; it’s an extra monthly cost to do what you can do at home with a wireless router). Both devices would hold basically the same amount of content relative to their same size counterpart.
Do you have Wi-Fi at home? It usually makes more sense to stream videos than to download them to the device permanently (although it is handy to download them to the device temporarily on occassions where you will not have wi-fi access). I think the average is about 1 GB of space per hour of programming. Books take up even less space as they’re just text. Even with the 16 GB, you could fit thousands of books.
Both the Kindle Fire and iPad have backlit screens, so there is no need for a separate light for nighttime reading.
Closed captioning has more to do with the service providing you with video content than it does the device. Amazon Video (which you can watch on either the Kindle Fire or the iPad through the Amazon Video app) is somewhat lagging with regards to offering closed captioning. Netflix and Hulu Plus are both better (though I would ranke Netflix abve Hulu).