I currently use Sequel Pro for database management on remote servers.
To keep things secure, it can only access the mysql databases via SSH. This has two modes of operation:
1. Entering the host and port that SSH is listening on, with the SSH username & password
2. Entering the host and port that SSH is listening on, and the SSH username.
In scenario 2, the system automatically detects that I've setup my client system to authenticate via authorized public key. (I think it uses the background ssh-agent, but I'm not certain).
I'd love the above to be built into MySQL Compare. Without those features I can't easily use MySQL Compare for any staging or production servers.