These are all Android based devices but the difference is whether or not they run Android TV or not and how difficult it is to load the Kodi app. If you want to use the device for all kinds of services other than Kodi (let's be honest, just HBO Go really) then you don't want an Android TV device - at least not today. Android TV is a very nice platform but they've been promising to bring new services like HBO Go to the device for almost a year now without actually delivering.
If you just care about Kodi, the Google Nexus Player is an excellent choice at just $79. It also has the easiest path to installing Kodi. Similarly, the Nvidia Shield TV has the same easy install path but a Tegra x1 processor and gaming controller if you're into Android gaming. Also, if you want to gamble, these will be just fine if/when Google actually delivers on these services.
The better options in my opinion are the Amazon Fire TV devices. The Fire TV Stick is basically the same as the standard except with less RAM, a slower processor, and fewer ports. It should still run Kodi pretty well though if you're on a budget - it's just $39. For me the Fire TV is the way to go though. It's got HBO Go along with all the other standard services, and since I'm all in on Amazon Prime anyway, I get a first class experience for the free services that come with Prime (Amazon TV, Amazon Music). There is no need to jailbreak the device and the hardware is top notch. Combine that with Kodi and I've got a modern piece of hardware that does everything I want for around $100.
The Kodi installation process is a little more advanced than what some people might feel comfortable with, but if you were willing to jailbreak your Apple TV it's still an easier process. Using a desktop program called adbFire you can push the Kodi app to the Fire TV without having to mess with the command line. There is a step-by-step guide here for doing so. Just follow the steps carefully and you'll be up and running in about 10 minutes. For those comfortable with a manual installation, the process can be even quicker and has the added benefit of being able to upgrade the Kodi package more easily later on. Those steps can be found here under section 3.
Regardless of the device and route you choose, there is little doubt that having a new and stock device is going to be a more maintainable path moving forward. Being able to update the device OS regularly will ensure you get the maximum life and value from your purchase and you'll also have a more stable experience as well. With the sunsetting of Kodi for Apple TV and the emergence of new options that are greater than or equal to Apple, it no longer makes sense to jailbreak your Apple TV moving forward.
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