I’m not surprised the databases aren’t compatible. There are enough differences, like history saved in the database across sessions on max and not on windows that I believe the structure is different.
Also there’s the whole problem that the database image file index is dependent on the serial number of the hard disk where those images are stored, it’s unlikely the database itself will ever be transferable across platforms.
That said, aside from information about cached images, and a cache of the data available in a DOP and or the metadata of the original image file, the only thing that I can tell that’s kn the database and not in the sidecars is information about an image’s project membership. (And the advanced history info.)
You can vote for adding project info to the DOP file here. This would make it relatively easy to maintain to separate databases on different machines and still be able to go back and forth from machine to machine to edit as the sidecars will have the edits (assuming you have the sidecar settings correct on both machines.)
Vote here: