One big advantage is that Shared Folders work even if networking support is disabled. You can, for example, set up a VM with no virtual NIC to simulate a PC with no Internet connection, or you can disable the virtual NIC, but you can still used Shared Folders to get at files on your host. Shared Folders also keeps working if your PC becomes disconnected from the network, where bridged connections do not.

Another advantage is Shared Folders use the security privileges of your HOST, not the GUEST. This can be useful to access Windows domain resources from a guest that isn't part of the domain. This can also be useful if your VM can't access the domain resources directly due to technical limitations (no support for Active Directory, etc). You can map domain resources onto the host, then share those resources using Shared Folders into the guest.

I mostly use VMware Workstation on Windows, but I'm sure there are similar situations on a Linux host/guest where the Shared Folders feature can let you work around networking issues if you just need to get some files in and out of the VM.