I don't know. The time it takes depends upon so many factors. Is CCC backing up every file every time? That would take forever! Assuming CCC is instead doing incremental backups, I would guess its speed would be similar to Time Machine, if they were to back up to the same destination over the same throughput WiFi link.
(You probably know that after the initial backup, TM will back up only files that have changed. I expect there's a way to do that in CCC too.)
What's the destination for your CCC backups? A Mac on the local network, a NAS device? Maybe that's the slow point. If so, a Time Capsule (in conjunction with TM) could be faster. But it all depends...
I'm a very happy user of TC and TM, for five years now. I love this setup. My 2008 iMac and my 2011 MacBook Pro are backed up to the TC (wired and wireless, respectively). I haven't noticed any long wireless backups except when I'm near my "G" access point instead of my usual "N" access point -- then it's noticeably slower, as would be expected.