Congratulations on your upcoming child. The unfortunate answer to your question is that it depends... I would say in general, I think the FSA is the better method for 1 child. Your income level will determine which is best, however.
The effect of the FSA is to take $5000 off of your taxable income. If you are in the 12% bracket, you are basically getting a $965 benefit ($600 Federal, 365 Social Security). The benefit obviously grows the higher tax bracket.
If you do the dependent care credit, you get 20 - 35% of up to $3000 in expenses as a tax credit, so you are looking at a benefit of $600 - $1050. My reading suggests that the 35% is for income $15000 or lower and it decreases by 1% for every $2000 of additional income until you hit $43000 and stays at 20%, so that should help figure out your benefit.
You should be able to run some basic calculations, but I would say if you have more than $21000 (level where you get 32% tax credit) in taxable income, you definitely want to go with the FSA. As you look to the future with a second child, you can take the FSA and do the dependent care FSA for an additional $1000 in expenses ($200 - $350 credit).
Hope that helps.
