People do buy servers with lots of hard drives in to use as network storage. The main difference is that you then have to manage that server and the underlying OS - a NAS is specifically designed to do one job and, in theory, should be much easier to manage than a full blown server.
We've just brought a couple of Sun X4500 'Thumpers'. Maybe not what you'd call cheap but with 48TB in a 4u box you certainly get a lot of 'bang for your buck'! The downside is that you've got to manage Solaris, setup CIFS, NFS, iSCSI ...
We also have some Netapps which we use as good, solid NAS boxes. Easier to manage but not so much 'bang' with those ;-) Also, the OS on those is designed to do only 2 things - store and serve data and there is a lot of functionality built in to do that very well.
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It depends on your management expertise. If you are well versed, you can probably set it up once and not have to worry about it again, just like a NAS. The NAS has an embedded OS which is very simplified. But it's just about the same thing you could do with Linux and a few apps.
If you >don't< know what you're doing, then in the case of building a Linux box, you may run into security vulnerabilities and have your system compromised and all your data stolen (which could be a huge security risk if you have your other systems backups/passwords on there).
Depends on the NAS and what you're looking to do. An enterprise NAS is going to be faster than any small box you can just throw together. Typically they'll integrate much better than a home-grown solution as well, and provide things like clustering.
BUT, if you're just looking for cheap, 99% of the time a box full of SATA disks is going to be *good enough*. I know I can push 100MB/sec easily on my homebrew solaris box.