The Note 10.1 2014 looks to have a 2560 by 1600 display so any mirror when resized to 1080p would be incorrect.
Right out the gate "MIRROR" would fail to deliver what you are after.
I'm unsure how long you've been around Android but codec support is growing but there's a reason why it is not on par with say VLC Player. I can't tell if you know why but let's hear from you if you know why. Why?
Because of a snafu with the Note 8's version of Android, mirroring to TV through MHL is note the correct aspect ratio - sides are cropped off - little blacks bars at top.
The stock android player mirrors video perfectly fullscreen but has crappy codec support - and thus is useless to me. All third party players like MX Players are similarly cropped.
So, before I buy the Note 10.1, I need to know if it's version of android shares this problem. Specifically, I want to know if third party players mirror perfectly fullscreen?