Just to add additional information: you can't use the childcare tax credit if you only have one child and have an FSA. But the childcare tax credit for one child only deducts up to $3,000 of childcare costs and the FSA gives you $5k tax free. (If you have two children in childcare then you can use the FSA and also deduct $1k with the childcare tax credit.) Also, the childcare FSA reduces your income according to Social Security because it is also exempt from payroll tax (7.65%).
So if you're in the 25% tax bracket the FSA saves you 32.65% * 5,000 = $1632. The childcare tax credit would be 25% * 3,000 = $750. I think almost $900 is worth it for the extra hassle!