The original headline feature of unilog was that it wouldn't block writes if the disk filled up. multilog does - if it can't write a line to disk, it stops ingesting data off of stdin, which eventually causes the application to hang writing to stdout.
unilog sends you an email and starts dropping log lines, which we decided better matched the tradeoffs we wanted to make - losing logs sucks, but not as much as blocking your application until you figure out how to free up disk.