log_size sets the maximum number of log events to buffer in memory for delayed viewing (currently in web interface only ?).
log_file_size sets the maximal size for log file, in megabytes. Beware, that limit is only checked when the core is started, or when this option is set, so it's not sufficient to handle large logs resulting from long running cores. You could set this option periodically to enforce the limit; However too large logs are simply cleared, no proper log rotation is implemented, so it would probably not be satisfactory either.
Alternatively, I suggest to use logrotate (linux's service/utility) to take control of mlnet log file.