The nexus player is pretty good tech for the price
I got one for $50 and it's ran with out issue for me.
The devil is always in the details. There are some cheap Android boxes that do have very good processors, etc. But you must compare each element - particularly the GPU and hardware decoding features. Often it comes down to small things like Bluetooth or remotes, etc. I'm very happy with my cheap Android boxes.
But the most important difference comes down to the brand itself. With cheap Android boxes you will often have trouble with streaming. It turns out that services like Youtube and Netflix will only stream HD content to "recognized" devices. Check out their web sites for details - they will have a list of devices like the NVidia Shield that they will stream HD content to - the Android box won't be on it. The streaming experience from those services will suck. But it isn't a technical limitation. So HD life is just fine if you download content or stream from some of the "free" services out there.
You can look at a full comparison here . Bear in mind this is written by Nvidia, so ignore the highlighting because it's deceptive. E.g. it's a green cross for Amazon instant video, even though that's a downside. But it's a fair comparison, they didn't leave anything out.
Performance
Generally the shield will be snappier (better processor), faster to load videos (better ethernet port, providing your router isn't a bottleneck).
Openness
Getting Kodi on a Fire TV is not easy, the scripts to load it break on updates, you won't have Google Play on a Fire TV (although you will on a roku, and it's the only one with Amazon instant video).
The two difference that I care about:
4K at 60FPS
Nothing else will stream 4k at 60fps. You'll have to own a 4k TV for this to make a difference, and you'll have to source 4k content (more and more content is made in 4k, but most things aren't).
In Home Streaming
The nvidia shield has an onboard h.265 decoder for Nvidia GameStream .
Basically if you have a PC with an nvidia graphics card of a sufficient spec in your bedroom, you can stream games to your living room over the network.
You can do the same with moonlight stream on any android device, or using a steam link (the link works for any graphics card). But those both support h.264 and not h.265. Therefore the stream quality will be worse.
The Shield is also marketed as a console, so it comes with much nicer GPU hardware (Tegra X1) that has decent gaming capabilities.
Performance
One of them is a beast of a product from a reputable OEM, the other is a plastic box of smartphone components soldered together by some random Chinese company.
They're also running two entirely different operating systems from Google. "Android TV" is not the same as Android on a touchscreen device. That doesn't stop these companies from marketing their TV boxes that run Android as an "Android TV box ".
Thanks for all of the info guys, these comments have answered pretty much all of my questions
The Nvidia shield TV is android tv, while the box is just a box with Android phones os. The Nvidia shield TV is much better, better hardware, better support and a better value.