And you could still use LVM to make a sane, fast, performant snapshot of it either way.
No, you can't.. Do make sane snapshots, you need application-layer support, especially for databases. Otherwise your snapshots are not clean, they are in a crash-recovery state as far as the application is concerned. This is particularly important for databases, distributed file-systems, and queue-based software (including mail stores).
The beauty of the Microsoft Volume ShadowCopy Service is that it is a stable API through wich applications, backup software, and storage systems can all communicate. Backup software says "I want a snapshot". All the applications who have registrerd themselves with VSS get their writes flushed into a consistent state, and say "I am ready for snapshot". Then the storage device (either a software filesystem like NTFS or a SAN/NAS) says "I am doing the snapshot". This level of coordination is simply not possible on Linux.