CheckDB does a CheckAlloc on the database, a CheckTable on each table and view, a checkcatalog. So I think there is a chance that checkTable won't catch problems that a full DBCC CHECKDB will. And that's obvious; a DBCC CHECKDB takes more time to complete because it's a more in-depth check.

I do not use CHECKTABLE when checking my databases, I always use DBCC CHECKDB. If my database is too big, I use PHYSICAL_ONLY flag. But still, I perform DBCC CHECKDB at some point.

Also, I use a Dev server for that, not my live production server. Unless you have just a few databases and they are small ones (below 50GB), running DBCC CHECKDB will take hours and will have a negative impact on I/O performance.

So, my 2 cents:

-Backups and restore your databases to a different server if possible (a non production one)

-Once restored, run a DBCC CHECKDB on all of them unless they are big.

-On big databases run a DBCC CHECKDB WITH PHYSICAL_ONLY but try to run a full DBCC CHECKDB at least one time every month.

Doing that you won't only be checking database integrity but the integrity of your backups as well. After all, you can only fix a data corruption problem (without data loss) if you have a good and recent backup. If you have not tested your backups and they fail, you pretty much are out of luck and it will be a very long day indeed.