I have 10 year old and 13 year old, they both like their kindle fire. We also have available for their use a 10" touchpad running andoid, and a couple ipads. One of them also has an ipod touch and the other has a wifi only iphone 3gs hand me down.
Personally I am not too thrilled with the fire and really don't understand why it isn't better integrated into the Amazon ecosystem with cloud based categories and better segmentation of books from a shared family library. But they like the size and ability to use it for reading and games, they take them everywhere.
The fire tablets were purchased for $149 last year before Christmas, perhaps they would like the nexus 7, but I think they actually like the simplified interface on the fire and the fact that I keep adding books I get free from eReader IQ which show up on the carousel...
Yeah, the Kindle Fire (original models) seem lacking in certain areas which is why I'd prefer the Nexus 7 over them unless they were priced substantially less. Besides, when the wait isn't absurdly long, I'll be getting a Kindle Paperwhite for reading, so that feature of the Kindle Fire is decidedly less enticing.
As for the person who responded about a DVD player for my sister...you realize that you don't have to leave the tablet attached to the headrest in the car. You can, you know, remove it and actually use it for other things. A Kindle Fire / HD on a firesale price could pull double duty and still be reasonably easy to replace even if the kid did manage to break it one day.