It’s not a performance related decision as, besides some overhead, performance will be the same. In general you would want to get as much backup consistency as possible; application-consistent > file-consistent > crash-consistent. There might be reasons for crash-consistent backups, like limited permissions, lack of application support or the guest OS doesn’t support it (like Linux). Also some VMs might be very static and don’t require more then crash-consistent backups. But for all other cases, go with application aware processing if you’re able to.
Regarding your initial questions. I wouldn’t try to directly backup the VHD(x)s on filelevel of the Hyper-V itself. The disks are in use and neither Hyper-V nor the VMs will be aware of the backup. So, you might end up with corrupted/unusable backups.