I should have said in the initial post. I had problems with my mid-'12 MBP and had to revert back to the previous OS before the BETA version of Mojave. I bet my external hard drive settings were reset and I have to start fresh. I went to www.wd.com and there is no listing of software for a Mac running Mojave. I'll keep an eye on it though.
Well if you CCC to the External. Boot off said External to the new machine. Then CCC to the new Mac. You'll have an exact carbon copy of your old computer on faster hardware.
The real advantage is in the restore process. I've lost count of the number of times Migration assistant failed a restore or mysteriously hangs for hours on end. With CCC you can see a progress bar. If it hangs you can see which file it is hanging on. I forget if there is a setting to skip errors as I use Freefilesync. I prefer clean OS installs, clean app installs and restoring only data.
"Does CCC do a better job if moving everything to a new machine?"
I can't answer with assurance, because I've never used Time Machine to backup, not once, and will never use it. (I've even removed the Time Machine app and preference pane from my Mac).
I use ONLY "cloning apps".
But, yes -- I think a recent CCC cloned backup (you could also use SuperDuper) would be better, because I've read reports that when using setup assistant with a new machine, it will go faster.
I've seen numerous reports of trying to do a migration with a TM-based backup and setup assistant just.... hangs... towards the end -- it won't "complete".
I'm going to GUESS that a potential problem with trying to migrate from a TM backup (which may contain many copies of essentially "the same thing" over and over) results in setup assistant having to "pick through" each saved version of every file -- and then try to "sort it all out".
With a cloned backup there is none of this, as there is only one copy of every file to be migrated. Faster and easier to "sort out", because there's "nothing to sort"....