Hm... well, for my mother, I don't think a more restrictive OS is much of a problem. Like I said, she'd mostly be using it for casual stuff and being able to watch Amazon Prime stuff would be a huge boon for her (I think). And from what I've read, you can still put most any android app on a Fire, so if the stock browser really is that bad it shouldn't be too hard to get an app for a different browser, right?
The biggest downside to the Fire (that I can be aware of without actually seeing one) seems to be the very limited UI--the "carousel" thing sounds really stupid to me, but apparently there are some options that make it more tolerable. As for the OS itself, from what I've been looking at there doesn't seem to be a sufficiently appreciable difference between Android proper and Amazon's Android--the main difference re: Nexus 7 is the 7's slightly better hardware and greater customization options, the latter of which seem more important.
My mother is used to Apple's mobile UI, so it may be better to get her a Nexus 7 just because the UI is so much more similar to the iPad's....
"...Blame this on the misfortune of your birth." -Char Aznable
Got both Nexus 7 models, love them. The new one is noticeably better if you compare side by side or play on it first, then try the older model, but the old one still runs great and runs better then the Kindle Fire imo. One thing I think the Kindles have over both Nexus 7 models are the built in speakers. The newer Nexus is way better than the original, but still not as good as the Kindles imo.
I have a kindle fire HD 8.9, I use it primarily for reading, watching prime movies/shows while running at the gym on the elliptical. Furthermore I use it for storing school documents on, such as papers, documents, books, presentations, etc.
I purchased the HD with the intention of using it as a media consumption device not a media creation device, if I wanted to use a tablet for work related purposes such as coding, writing extensive documents, or networking then I would use a Microsoft Surface.