New Time Machine volumes in Monterey will always be formatted APFS by Time Machine, as
@NoBoMac indicates. So no choice there (unless you try to have the new machine continue using the old machine's TM backup -- which might be possible but I wouldn't recommend.)
For CCC, you might need to use APFS if you're planning on making a "legacy bootable backup." However, Mr. Bombich doesn't recommend that type for most uses (sorry don't have the link handy). IIRC, he recommends first re-installing macOS (from Recovery or Internet Recovery) and then using Migration Assistant with the standard CCC backup.
Ah, found a quote from the link I cite below:
Personally I've given up on making a bootable backup for my Monterey systems. Here are some reasons: (from
https://bombich.com/kb/ccc6/cloning-macos-system-volumes-apple-software-restore)
If you decide to make a "standard" CCC backups, I see no advantage to using APFS for the destination format on an HDD. In addition, I think there are two (admittedly small) reasons
for using HFS+: (1) it's possible that an APFS file system bug could arise that doesn't occur in HFS+ and (2) there are tools like DiskWarrior to deal with accidental erasure or partial corruption on HFS+ drives, but no such tools exist for APFS.
So I say, with one backup on APFS (TM) and one on HFS+ (CCC) you're protected against a greater number of possible disaster scenarios.
This is also why I use both TM and CCC -- not only do they have different strengths and weaknesses, but it is possible something could go wrong with the backup software itself that renders a backup unusable. (IMHO this is more likely to happen to TM than to CCC, but still, it's possible.) So I think you're wise to use both TM and CCC (or SuperDuper!).
Sorry if it seems like I'm "talking your ear off!" Good luck!