really; there are three different circumstances regarding this question; "it depends".....
1--at the entry level it’s a horse apiece.....computers are servers. servers are computers. maybe a dedicated server has slightly less noise, and maybe a better power cord than a sever; but likely your network bandwidth, network switch, ethernet and usb cables will have a greater effect than other choices at this level.
2--mid level dedicated servers will outperform regular computers and laptops since they eliminate much of the peripheral noisy processing duties of the normal computers. there is a clear difference to go dedicated.
3--price no object server levels they far outperform any computer or laptop. but you are talking $20k to $100k for a music server. i own a $76k music server and it is awesome sounding and significantly outperforms my previous $30k+ music server. once i heard the difference i could not 'unhear' it. and took the plunge.