3 kids, baby sitter cost 5,800 a year, making 150k, better for me to use flex spending account for babysitter since is pretax, or child credit?

I have 3 kids, I pay baby sitter (5,800 a year).  we make around 150k a year.  Someone told me that it will be better for me to use the flex spending account to pay for babysitter since is pretax, than paying directly with checks and then claiming the expense in my taxes.  what will be better for me? When I did my taxes this year turbotax said that we didn't qualified for the child credit because of our income braket.