Is it true that binary backups always take less space than text backups?

Yes, because binary backups only contain data, and not statements required to insert data into the tables.

No, because text backups can have optimizations, which make them smaller, such as updating many rows at once.

No, because if InnoDB tables contain many empty pages, they could take more space than the INSERT statements.

Yes, because even if InnoDB tables contain many empty pages, text backups have empty INSERT statements for them.