You are smart to "prefer to have the drives formatted to the right operating system".
What (I think) you actually want to do is synchronize music libraries (and maybe other documents), obviously a straight clone from one OS to another won't work very well.
On Mac OS, I use an app called "File Synchronization"
nemesys.dyndns.org. It works great for keeping my libraries in sync between my primary computer and backups, and it will definitely work with shared volumes (also with thunderbolt or firewire target disk mode). I've never tried it with a shared Windows volume though.
I've used that app for years, it's always worked well for me. If you try it, be sure to learn all the functions..."delete orphaned files" is very relevant to keeping a media library synced, for example.
