This has been discussed here 100000x times so here is summary/comparison.
TL;RD version: you need both...
1. Time Machine is unique backup which does not have to be fast, it is continuous backup, working always behind you back. It is perfect for routine users, it is free, generally works (yes, disks get corrupted sometimes, but that happens with EVERY disk once in a while). I did my best to find similar software on Windows years ago and even though some exist, they are never as smooth, easy to use, and as result useful. They are ridiculously difficult to use in case of disaster, which is strength of TM. So use TM - it is excellent for periodic backup. I have two - one at work and one at home.
2. Carbon Copy Cloner or SuperDuper are excellent backup solutions which create bootable snapshot of current system. They are very useful to keep complete snapshot of the system at given moment in time (=before upgrade, for example), but they are not as good to be able to go "back in time". I have two CCC backups (you guest it, one at work and one home) made once per week automatically.
If your system fails, CCC or SD backup allows you to immediately restart the system from the backup disk - possibly at somehow old time. If that is what you want, use those solutions.
If you are looking for old file use TM - my TM has last snapshots going back ~2 years. Excellent as cheap always on "version control" with limited granularity. Keeps 2 hours snapshots for some time, then daily, and eventually (further back) weekly until it runs out of space... Spectacular and dumb easy to use.
If your system fails and you have TM, you can wipe/replace the drive, install OSX on that and using migration assistant restore from TM. Takes lots of time (12 hours for me the last time - may be more depending on amount of data) BUT - you are within 2 hours of the disaster... It restores everything, even history of each application, it was amazing.