The new base quad core is faster. Not way faster, but a pretty good step up in performance, except that it lacks hyper threading so it depends on the application. The new 6 core i7 would be a much more noticeable improvement.
Plex Server is decidedly not a strenuous app. I am running one on an ancient i3 Thinkpad using Win 7. Cost me $65 on eBay. Mac equivalent would be pre-2009 powerbook. The key is not to be bogged down with other apps running at the sametime and for the files not to be ultra-compressed.
Does 2012 have HEVC? I could be wrong but dont think it does.
Theoretically, new Mac Mini will be more efficient for x265 transcoding, if needed, i.e. when watching foreign movies with subs. You’ll need plex pass to unlock hardware encoding.