Kindle is designed and controlled by Amazon - which is also tightly controlling everything about that tablet. The downside is the Amazon app store is not the entire Google Play store. The upside is since it is controlled by Amazon there aren't a bunch of willy nilly apps that could contain malware.
Malware went undiscovered for weeks on Google Play | Security & Privacy - CNET News
The Kindle App runs on pretty much any device and Prime Videos is available for the iPad. The Kindle lending library is not available on anything other than a native Kindle device. (All of this is only useful if you have an Amazon Prime membership.)
If you don't have any other Apple device or media then one could argue there isn't much difference for media consumption. If you do have Apple DRM media then any iOS device can play it. Plus if you have Apple TVs or other Macs there Airplay which allows you to stream media from one device to the other. There are other 3rd party solutions like Plex to do streaming but it isn't as integrated and not always bi-directional. (If anything new has developed in this arena I'd like to hear about it)
Apps - if you haven't bought any then again not much difference. I have bought many apps over the years so making a switch to a different device would require a repurchase of similar apps. Apps are available across all iOS devices you own - so I bought the expensive GPS app - and now everyone in my immediate family that has my App Store login has that expensive app and has turn by turn directions.
iCloud and iCloud integration has become quite usable with the latest version of OSX and iOS. Pretty much all native apps save to iCloud so you can access the data from any device logged into your iCloud account. Google has google drive and Amazon has cloud storage but they don't make their own Office software - whereas iCloud is integrated into iWorks (among other native apps)
TL ; DR - if you are looking for a media consumption device then the Kindle Fire HD is quite good for the price. The Nexus is a very good 7" tablet that is general purpose. The 10" iPad has a lot more Apps available - and can still be used as a media consumption device.
(Note I kept the discussion to stock devices, you can jailbreak iOS and root android and open a lot of other possibilities)