A brief update on the stuttering 'issue'. I've bought a TV hat and the stuttering with HD contents (over DVB-T, we aren't talking about network contents nor recordings or local files in general) is even worse than how it was with the Xbox One tuner. By what I know (but I may be wrong) HD contents should be MPEG-4 here in my country so purchasing the MPEG-2 codec should be useless while, not being a recording, I can't follow gedakc advices (thanks anyway!).
I've made some digging and I've found some threads like this or even more this one. Unfortunately, I'm still missing how to sum everything up...
EDIT: I've just checked and the HD contents which stutter are H.264 1080p while SD contents (absolutely fine) are MPEG-2 576p.
see post #12..that should solve your issues..