My friend wants to cut the cord and keep prices down to a minimum. So, essentially it's either a Shield or a MiBox. I only have experience with my Shield and HDHomerun Connect, and it's been pretty good.
I'm just wondering how the Mi Box does with Plex and Live Channels? Should I just advise her to go for a Shield instead? With Live Channels if she makes a recording on one Mi Box can she play it back on a different Mi Box in another room or are the recordings locked to a single box?
None of this OTA DVR TV Live Channels stuff matters when any hardware device you intend to view TV on cannot do TV video deinterlacing properly or reliably.
The Mi Box, even with the leaked Nougat Firmware has rubbish deinterlacing. Deinterlaced mpeg2 picture output is blocky, jerks about when the picture pans and is half motion that has massive problems with fast video movement.
Those that say its Ok have never seen high quality full motion deinterlacing on Windows or Linux hardware platforms - the same high quality as a normal inbuilt TV tuner produces.
No TV Tuner support on the Mi Box even with leak Nougat Firmware. Just upgrading to Android 7.0 is not going to magically add this sort of USB TV Tuner support. Xiaomi has to do it. I doubt they ever will - its a $69 box.
Even the NVIDIA Shield has problems with mpeg2 interlaced TV streams: https://forums.geforce.com/default/topic/1025974/shield-tv/mkv-playback-issues-since-upgrade-to-6-0/
Personally I would not use any Android Box for high quality reliable TV viewing / recording usage. There are better hardware options available with Dual Tuner setups that are far more flexible when it comes to simultaneous recording and viewing TV.
The Mi Box would be pretty shit if you could use it as a DVR. The storage is very limited. You'll need at the very least to tie up your one USB port with a USB drive to get a reasonable amount. If you want to use an android TV box as a DVR (if you have some software in mind, I haven't seen any that can be done all in one box) I would suggest the Shield Pro, or at least the basic shield with a micro SD card so you've still got some USB ports free.
I don’t think you understand plex...the pvr, like the rest of plex has nothing to do with whatever end box it is played on. The plex server, wherever it is, does all the work and the mi box/nvidia shield/AppleTV/iphone4/xbox360/ps2 or whatever you have at the end of the line just watches what the server casts to it. My plex server is an old PC running freenas with a bunch of mirrored drives in it, and the pvr hooked up to the HDHomerun works great and I can watch PVR shows anywhere that has internet access on my iPad and iPhone as well as my ps3, Xbox one and nvidia shield that are in my house.