The first thing to think about is that if you run a file system and file sharing protocol on your storage device (making it a NAS), you won't have to run it on the server. That's a little bit of work avoided. If the file system will need to be shared among other servers and users, this might represent quite a bit of work avoided.
If the server using the data is the only server accessing it, it's probably best to stick with block level protocols (FC, SAS, iSCSI, or FCoE). The main reason for this is that while the management of the actual file system is fairly easy for a system, the protocol to access that file system over the network can be hairy and inefficient. CIFS is extremely inefficient, and NFS, while more efficient than CIFS, is still much less efficient than anything based on SCSI.
If the data will be shared among many servers, your only choice for block would be a cluster type environment, where all the nodes have access to the same SCSI volumes. That may not be a possibility. And even if it is (for VMWare, for example), there are often advantages to having the file system and file sharing protocol handled by something central that's not a server.
Specific workloads where it makes a lot of sense to use a NAS:
- VMWare: the VMWare file system you'll install on a SCSI volume on everything before the latest version of VMWare is not very well designed, and introduces all kinds of limitations to your environment. VMWare bent over backwards to make sure they support VMDKs being hosted on NFS, and that eliminates the need for VMFS for a lot of shops. That said, there might be some things you can't do with NFS that you can with VMFS. I'm not a VMWare expert.
- Hyper-V: Microsoft's hypervisor's newest beta has support for the NAS, and it seems like it will be a priority for them to ensure that it works well.
- File servers: users' home directories and network shares are a perfect application for a central NAS. It's one less computer in your domain, and you can typically consolidate many file servers into a single NAS.