Music Server vs PC confused

I suspect the lack of replies might indicate the answer to your main question is no.  

For those of us hooked on Roon, a common setup seems to be Mac Mini running Roon core, ethernet to a Senore micro- or ultraRendu, USB to DAC.  A used microRendu is very inexpensive, and Roon will recognize it as an endpoint for receiving files.  A bit upscale is an ultraRendu; a matching UpTone linear power supply makes a nice package, but, IIRC, the pair is about $1K.

My answer is no. I have been saying NO to this so much that people must think I am a Sonore xxxRendu fan-boy (a Ethernet-2-USB converter or digital converter). They do work, even with a cheapo, busy, noisy computer in any room of your home, as long as it is connected to your network.

Look at at some of my past posts on this if you want to hear my propaganda on this issue.

Do you use ROON? The Rendu's are ROON READY.

I have not compared the two, but the usual argument for a purpose-built server is that a PC is running all kinds of functions you don’t need and is a very electronically noisy environment. All this noise pollutes your music signal resulting in lower sound quality. A music server is built to only deliver a more pristine music signal. YMMV

If you are using this as purely a "music server" only, then I think the differences will not be that great.  That means the computer can act as the sever (or file server), but you will need a DLNA Renderer/Player devices that accepts the streamed music data and clocks the data to generate the S/PDIF or USB pulses for DAC.

In your case, I think you'll be using it as both a Server and a Player, since you are connecting a DAC directly to this.  If you use a computer, many people have had good results with the JCAT USB card or other custom audio USB cards (think Paul Pang).  You will likely want to get the best power supply (linear power supply if possible).

With a stand alone music server, some of them have fully linear power supplies and good clocks for generating the timing on the pulses (for different bitrates and sampling rates).  The linear power supply makes a significant difference in the digital transport. 

If the mini PC is optimized to be used as a server, not needed functions turned off, and is fanless or doesn't  make enough noise for you to notice then I doubt you would hear much of a difference.