Dropbox Desktop vs CloudMounter, Cyberduck, Mountain Duck for Multiple Accounts - which is better?

"and not lose share permissions when moving files between accounts."

Welcome to the community flymenta​. I can't speak to the broader conversation of cloud managers, but in regard to the quoted section:

Sharing permissions generally will not carry over if you move or copy files from one Dropbox account to another, since they become new items under a different owner. If you need collaboration to stay intact, the safest approach is to work in a shared folder instead of transferring files between accounts.