SFTP is binary by default, that option is probably not available because your server does support ascii/text over SFTP to begin with.
The issue with Filezilla is somewhat related specifically to phpBB or anything else where a binary file does not have an extension. When you transfer a binary file in ascii/text mode it corrupts the header. Filezilla will correctly pick binary when an extension exists that indicates binary file but defaults to ascii/text for files without extensions. Why they chose to do that and continue to do that is beyond me because if you have a file of unknown content binary is the the safe choice.