A 2 child household gets $2k annually from the CTC.
A TANF 2 child household, at least according to liberals, gets $429 monthly. In, say, California, you get $694!
The math is obvious.
You also get to claim an additional dependent. TANF is also limited to 5 years for the adult while the CTC goes on forever as long as you have a child under 17. The math is not obvious. Not that it's about math anyway.
But the TANF person gets the dependent as well.
The credit for having a dependent isn't refundable, so if you don't have income to tax it doesn't do you any good.