I will answer the easier question first---Only the custodial parent is allowed to take the child and dependent care credit. The custodial parent is the parent with whom the child resides with the greater part of the year. Who claims the child as a dependent does not impact who gets to take the child and dependent care credit.
In answer to "how much is one child tax deduction worth"---When you claim a child as a dependent, you are allowed to subtract a certain amount from your income. In 2008, this is $3400. The actual difference in tax liability (bigger refund or less owed) that it makes depends upon your tax rate. For example, if you are in the 15% bracket, your refund would go up by $510 with the deduction. For dependent children under 17, you may be eligible for the child tax credit, maximum of $1000. Also, the total difference claiming a child makes can vary depending on tax rate, amount of income, other credits (such as day care and education) alternative minimum tax, earned income credit, and head of household filing status. If you have a specific situation, I would be glad to discuss it with you.