To answer the original question, my justification for a home server over a NAS:
1) You get more for less
+ It was cheaper than a 4 bay NAS
+ It's faster than a 4 bay NAS
+ It uses similar power to a 4 bay NAS
2) It's FAR more flexible
+ I can stream movies to several devices around the house
+ It can handle far more advanced RAID setups
+ It can just do a lot more - Minecraft servers etc
+ It's non-proprietary: if I want to upgrade the memory, I can
+ I can do more with it at once: web server, minecraft server, teamspeak, home media etc all at the same time
And my justification for having it over a PC
1) I can have it on 24/7 without wasting money
+ It uses a fraction of the power my PC does
+ Plus less noise
2) Less wear and tear on my (much more expensive) PC
3) It's server hardware, it's designed to be on 24/7
4) I don't want to slow my PC down with server duties
+ I don't want to slow my server down with PC duties
5) Separation of concerns
+ I can have the backup on the NAS with the primary copy on the PC. If one's PSU blows up and takes the HDDs with it, I still have a backup
+ I can turn the PC off for upgrades or tinkering, without affecting my server
6) Less vulnerable
+ Much greater control over the OS on the server
+ I only install required services, so there are less "ways in"
+ It's not a Windows server
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If you purely want your NAS for backups etc then great, get a 4 bay NAS. But too many people try to use a NAS like a server and wonder why it's rubbish.
Work out what you actually want to do with it and base your choice on that.