I've had no major problems with Gemini Lake Celerons for TV Headend server duties. I never run the Media Playback on the same platform as the server though (I try to keep media playing and TV Headend separate). My last TV Headend SAT>IP server was based around a <£200 Chuwi Herobox and a USB 3.0 external hard drive.
No need for anything like an i3/5/7 for TV Headend duties unless you are also going to do transcoding or run other stuff on it (not recommended).
As for why you see artefacts on some platforms or others - it's likely to be that some MPEG 2 Transport Stream processors and h.264 video decoders (assuming you're watching h.264 content) are better at concealing/correcting errors than others. You see very different artefacts when watching the same errors on different playback devices.