Well, it all depends on whether OP looking for something approaching audiophile quality or only for convenience. Just do the mini or Rpi he already has, do minimal cost free upgrades and compare the two.
The Rpi would be superior if willing to put out minimal amount of cash for upgrades, mini will require large outlay of cash.
Almost forgot, I owned Okto Dac 8 stereo with built in Rpi streamer, compared to my Musetec 005 going through SOTM SMS200Neo (both used mini as server only), Dac 8 was very, very nice, far better than my expectations at the time. While I was only using rpi as streamer, vs SOTM, rpi acquitted itself quite well against the $450 SOTM.