I just recently got an Amazon Kindle Fire HDX 7 32gb WiFi-only. This is the 2013 model that is a direct competitor of the Google Nexus 7 (identical price, screen, form-factor, memory, storage space).
I want to point out that my primary use for a tablet is nontypical, so what are deciding factors for me, may not be for others. Typically, I just want a tablet to read on (forums, schematics, scientific papers, encyclopedic articles), watch video (youtube, anime, netflix, livestreams etc), check Facebook, and write on (email, forums, lists/notes) while not at my desk. I love being able to get into my comfy chair or lie down in bed and do all the things I want/need to do. I don't use my tablet for gaming, drawing, or as a PC replacement.
As such, hardware is my primary concern; processing capacity, battery life, screen ppi/dpi, screen size, memory capacity, speaker quality, GPU, etc.
The key differences between the HDX7 and the Nexus 7 are this:
Nexus: True Andriod OS, poorer speakers, smaller battery, slower processor, slower GPU.
HDX 7: Amazon ONLY android fork OS, better (louder, clearer) speakers, larger battery, much faster processor, slightly faster GPU.
I did my research for over two weeks before picking which tablet to go with. I read dozens of reviews and compared each with scrutiny. All of the reviews and data said that both devices supported the same software, just that you would need to sideload some things that weren't in the Amazon store.
I went with the HDX purely for the better speakers and battery, betting that I wouldn't notice the difference in OS since I have nothing invested into the Google Play (Android) App Store or the Amazon App store, and that 90% of what I want to do on my tablet is native to ALL tablets and not processor/gpu intensive.
That being said, after having the HDX 7 for a week, two issues came up.
1) No native support for YouTube or Flash Video. The way Amazon gets around this is by having their proprietary browser, Silk, load up youtube videos in the amazon cloud, and stream the resultant video to you. Now, depending on your network and location, the amazon cloud can be really shitty at this. It is decent for me, but not all sites are supported by Amazon Cloud. Embedded video also isn't supported in Silk. Thankfully the site I use for anime is, and youtube is. Using Silk you are forced to using the Mobile version of YouTube, which does let you sign in and access all the subscriptions and playlists on your account. Unfortunately, the mobile version doesn't let you edit playlists (even the watch later list) or add things to playlists. Likewise you can't thumbs-up or thumbs-down of anything you watch. You also cannot comment, but you can read comments after the video is finished playing, not during. Pretty piss-poor implementation, right?
Now, with Flash, the hardware and OS itself DOES support Flash! Flash just isn't available from Amazon's severely limited app store. Nor are any other browsers. But, you can sideload Chrome and Dolphin browsers. So, you sideload chrome and it works flawlessly, aside from the fact that you cannot sign into Google and access any of the other chrome stuff from your other devices or account. Flash also doesn't work in Chrome. Go figure. It is possible a newer version of Chrome does support these things, but since I don't have an android device to steak the .apk from and have to rely on webhosted .apk's to work from, the only version I found does not.
Behold Dolphin! It is about as fast as I.E.8. So, yeah, not great. BUT you can directly download files in Dolphin just as you would on a PC in chrome. Additionally, it supports flash, and embedded videos once Flash is installed. And as such you can direct install flash from any site with a flash video when it pops up the error about not having flash. No need to go around looking for a flash .apk to work from.
So. I do most of my browsing with Silk, except when I have to input sensitive info that I don't want routed through Amazon's servers, in which case I use Chrome. If I want to watch embedded or flash video without having to go through Amazon's servers (either because they don't support that website or I don't want to trust their servers with that material) I use Dolphin.
Convoluted, yes. But I'm forced into it because Amazon has locked all of their devices in the Amazon Jail, and you cannot Jailbreak most of them (some of the 2012 models have been successfully jailbroken, but it is a high rate of failure and there is no way to unbrick the devices if they get bricked).
2) Exactly on the eighth day of ownership I noticed a small patch of dead pixels near the center of the display. It was triangular in shape and approximately encompassing about 18 pixels. I kept this tablet in pristine condition. It stayed in a soft padded case on my desk when not in use in my hands, and never felt so much as even a small bump. I even wiped the fingerprints off each night with a microfiber cloth. I contacted Amazon support with the onboard Mayday feature and reported the problem. They processed it immediately and set up a UPS pickup of the defective unit and a 2-day shipping of a replacement unit. UPS should be by tomorrow to pick up the old one and I expect delivery of the replacement on Tuesday.
I requested a full refund instead of free replacement but was denied because the unit was defective and had to go through the manufacturer warranty - not Amazon itself.
I can live with this because I was overall satisfied with the product for my needs, even with the convoluted workaround needed for Youtube and embedded or flash videos. I would have preferred to get a full refund and get the Nexus 7 instead though, just for simplicity and ease of software compatibility.
The HDX comes with a 1mo free trial of Amazon Prime as well, assuming you haven't had a trial of it before. This includes free shipping and up to 30% off purchases at amazon.com, as well as use of their instant streaming store for free. At the time that most of the info about the HDX was written, there was no support for Amazon Prime Streaming on anything except amazon devices. After getting the HDX I found out there is now support on all Android devices for this service, and you can now access the 1mo free of Prime without having to make a purchase.
So, if YouTube and selection of apps aren't important to you, but a simpler interface/OS is; go with the Kindle Fire HDX 7/8.9 or the new Fire HD 6/7. Otherwise, go with the Nexus 7, you won't regret it.
I'll enjoy the HDX 7 (replacement) because it's a pretty close fit for my needs, and I can't afford to go out and spend a lot of money on another tablet. Next year or perhaps in two years when Google has their latest and greatest tablet, I'll go with it instead. This was my first, and last, foray into the Amazon Ecosystem. If people manage to successfully jailbreak the Fire HD/HDX systems or Amazon tears down their walls, fantastic! If not, I'll live. It still beats not having a tablet, hands down.
edit: Btw, I am heavily invested into the Apple ecosystem, and love my iPhone 5 (and loved the 3GS before it), but their tablets are incredibly expensive for what their hardware offers. The original generation iPad, which is now four years old, is still $200. That's how much a 2013 Nexus 7 or HDX 7 is. If I could have afforded an iPad Mini or newer, I would have gone with it instead, but given how expensive they are it is very hard to justify when you're on a tight budget or not invested into the Apple world.
