Connected to my gaming pc via ethernet, does the Shield perform significantly faster? It costs $200 more than the Mi Box in my country. Main uses: watching 1080p movies and occasional gaming. I never use streaming services because my connection is very slow.
I have a Mi Box but I don't have a Shield so I can't compare them.
I've been using Kodi to watch my movies (1080p h264 and h265) that are stored on my NAS: no problem as long as your connection is good. My Wifi was too slow so I had to buy a USB to ethernet adapter. However, when I upgraded my Wifi to 5Ghz Wifi, no more problem, it's super fast over Wifi now, I don't need the adapter anymore. I was using a raspberry pie before. The Mi Box is way better: Android TV is pleasant to use, the Mi Box remote is quite good too, and it's quite fast, no slow down.
I tried Steam Link for an hour, using the Steam Controller connected to the Mi Box via bluetooth. My computer is connected via ethernet. I've played Lego Star Wars and Project Cars. It was an overall good experience, no bug, no freeze. On Project Cars, I think there was some frames drops, but I don't know if it comes from my computer (it's not a crazy machine, i5, 8Gb DDR3, GTX 960), the connection or the Mi Box. Or maybe even Steam Link app.
I know the Shield is better, of course, given its price. It depends if you're willing to spend that much on a TV box.