I use both. From what I hear Carbon Copy Cloner is functionally the same as SuperDuper!
I see SuperDuper! (or CCC) as a good catastrophic failure backup. If the hard-drive crashes suddenly and totally, recovery is easiest with SD!. You simply put a new HDD into the system, boot from SD! backup, and "clone" your system back to the new HDD. I've also been having issue lately with needing to "repair" my system HDD file structure. I've been booting off of the SD! backup rather than install disks.
TimeMachine is for recovering files individually (in my situation). Because it keeps a copy of everything going back as far as space allows, I can recover a file from a week ago or a month ago. If you delete file today, then the next time SD! runs it is deleted from the SD! backup as well. However TM will still have it available.
In conjunction with each other, if I have catastrophic failure in the middle of the day, I should be able to use both SD! and TM to recover to the point of the last TM backup.
Hope this helps.