A few things no one has mentioned yet:
A big advantage of CCC over TM is that CCC backups are mirror images of your boot drive. The advantage to this is that you can directly access your files and folders on the backup drive. So if you accidentally delete a file or folder on your boot drive, you can jump to the same folder/file on the CCC backup drive and retrieve it in seconds. *Very fast and convenient.*
cf. TM backups are a black box. And sometimes reverting back can be more fussy and time consuming.
CCC also has a snapshots (restore points) feature, which allows you to roll back your boot drive to a specific time. The snapshots are very efficient and customizable. You can create, say, hourly snapshots, which then get pared down to just daily snapshots for X number of days, then weekly snapshots, then monthly, etc. And you can limit them to a specified amount of free drive space.
I use both TM and CCC. TM is great for restoring previous versions of files. And it's a great, hassle free way of automating your backups.
But CCC is faster and easier for restoring a crashed drive, or specific files/folders directly. 99% of the time, I'm using CCC.
Also, I use CCC to send customized backups to different drives and locations, e.g. some files are updated to Dropbox, photos are synchronized between three separate drives, bootable backups are staggered between 3 different drives as extra insurance. [The reason is that I'm also running MacOS on a Hackintosh, where a simple system upgrade can brick your computer if you're not careful]
When I get a new Mac, I'll still keep using CCC (albeit probably just with one bootable backup drive, not 3). And I will of course keep using TM.