There are upsides if this is going to be asleep or idle for most of the day. The usual notion for desktops is that they are on and being loaded down. But if is standby/idle is significant part of day it it is an issue especially if place it somewhere with limited ventilation and quiet.
HD5000 vs HD4000 isn't much of a job especially when it comes to video playback (i.e. no advantage).
If the new mini gets HD5000 series. I don't think that is a lock. Intel has priced may of the 5000 series CPU+GPUs outside the range that the Mini has a budget for.
Not sure if transcoding is limited to just x86. But yes confined to just playback it current Mini is capable.
Frankly even the Base mini should be fine for a media center.
If a sever if limited the number of clients shouldn't be a problem. If only the attached devices in the media center than should be fine.