haven't seen how Minix UI performs. but interfaces are lacking in UI. and it has no USB 3.0 -- should help play 4K HDR movies without any glitch.
for the Mi Box III, I've seen it and Shield still performs better PQ-wise. with Hi-Media Q10 Pro, you can put in a 3.5 internal HDD, right? it performs very good as well.
among those mentioned above, Mi Box III & Shield are the only ones that are Google-certified Android TV's. Shield would also allow you to play games as it's also a gaming console -- D-Pad controller, is included. =)) thus the price difference is very much justified with the Shield.