I'm not very intimate with the security aspects of Samba on Ubuntu, though it is an industry standard, and should be relatively safe. I also suspect that the File Sharing feature on Mac is basically just setting up Samba (or something very similar) on the Mac, because smb: is the standard protocol for accessing Mac shares.
If you use the Mac the most, I'd set up file sharing on the Mac, and then just access the share from the Ubuntu box when needed.
Edit: There should be something called Samba Client or similar for Ubuntu, which helps accessing the Mac share.