2019 vs 2022 devices It's like iphone xs(10) vs iphone 13
Xiaomi stick 4k have newer hardware and software, Better performance, speed, AV1 Decoding etc...
BTW. I have both
Chromecast with Google TV
I have the Xiaomi 4k stick, have had the Shield, ATV 4k, CCwGTV, Max, Cube 2, Mecool KM2 etc. The Xiaomi is just fine. Runs and plays without any problems. For me at least. I found the CCwGT to be the buggiest for me.
It depends on whether or not you'll need the ports which the mi box provides (USB 2.0, 3.5mm/optical audio). If you don't need ports, the stick is probably a safer bet. In terms of performance I doubt you'll notice a massive difference and you can probably find a mibox sold locally for a lot less than the new stick/mibox.
Why are you comparing a 6 year old device with a recent one???
No experience with the Mi Stick, but the MiBox is absolutely without the buggiest piece of hardware I currently own.
Firestick 4k Max or Firestick 4k...
Neither, get a Shield.