" I can't seem to wrap my head around it!"
That's because the great American tax system has become convoluted mostly due to politics.
As you can see from the numbers above, the EITC potentially provides more money, but as you income goes up that changes.
You don't have to choose between them, you get both (except in the case of divorced or separated parents). The EITC amounts are totally refundable and you get the amounts in the table, regardless of your tax liability. The Child Tax Credit it is a nonrefundable federal tax credit, but, if you have more than $3000 of earned income, some or all of it is usually given to you thru the "Additional Child tax credit". That is, part of the CTC may be on line 43 of form 1040A instead of line 35 (lines 67 & 52 of form 1040). The ACTC is calculated on form 8812 and is basically 15% of your earned income over $3000.
