I think it will be a marginal difference, chances are that even though the Macbook can run off of batteries, in a Music Server environment you are most likely running it off of a power supply.
I run my Squeezecenter server on an old Powerbook G4 which is on 24/7, and have recently experimented with running iTunes out from my iMac through firewire to a Focusrite 192/24 interface using Pure Vinyl as a player, and the iMac/iTunes/Pure Vinyl sounds better than the powerbook feeding the Squeezebox. Although both of them sound very good and enjoyable - just very subtle differences.
I would think the lack of fan noise and potential monitor/display interference would give the edge to the Mini (assuming it is in the listening room), even with the potential for running off of batteries with the MacBook. I think value-wise, for a pure music server application, the Mini would also win. You'd pay for a lot of stuff you don't need/use with a MBP server.
It would be interesting to hear perceptions from any direct A/B comparisons.
Jim C