They both have very different uses. DAS is used to attach a group of hard drives directly to a physical server. This machine is the only one which can access the drives, unless you setup a network share (Windows) or a remote mount point (*nix) to allow other machines access over the network.
A NAS is accessed just like a remote server on your LAN. In the Windows world you access it via \\NASName\ShareName and in the *nix world you’d access it via a remote mount point.
NAS are great as file servers because that’s what they do best. The take snapshots so you can recover the users data quickly without having to go to tape. They have a lot of cache so you don’t have to go to the disks often, but when you do the disks are very quick.
DAS on the other hand usually doesn’t have any intelligence at all. It’s just a bunch of disks (JBOD) attached to a server so you have to setup backups and RAID levels your self.
For things like serving web pages NAS units are great. You put a bunch of web servers in front of them and have the web sites all point to the NAS. However for databases, they aren’t so good because databases don’t like accessing there database files over the slow Ethernet network. They need fast direct access like a DAS gives you.