Server.
Size: My little VIA XP system lives in a case I cannibalised from a HP nas/media box. An off the shelf nas will be smaller but not by much.
Power: Without disks a typical nas pulls 10w to 15w, my little server < 20w
HD format: This was a big one for me, my little server uses NTFS so the disks are interchangeable with my other pcs. NAS boxes may use: FAT with the associated file size limit; ext2/3 nice file system but not interchangeable without additional drivers; custom ext which is a pain; other which is an even bigger pain.
Access: Using vnc I have remote access to a full Win XP system, this has proved very useful.
Cost: I had a spare copy of XP, hw < £200.
Noise: One fan on the cpu run at 5v - inaudible. Drive noise depends on make/model of the drives. The metal work of the case is enough to keep the drives cool.