In general, wherever folders can be used in Beyond Compare, profiles can be used as well.
In the Browse for Folder dropdown, pick Browse Using Profile to open a dialog. You can pick Local File System to browse for a local folder. In the Quick Connect folder, you can pick FTP Profile or Subversion Profile, enter the necessary login information, and click the Connect & Browse button to browse for a remote folder. You can also pick a named profile to browse for a remote folder.