There's no credit without it. Omitting Social Security numbers while still claiming the credit will result in a summary assessment of tax liability against you. Several limits apply. First, qualifying expenses are limited to the income you or your spouse earns from work, using the figure for whomever earns less. If one of you has no earned income, you will not be entitled to any credit.
Credits are always more valuable than deductions.
As you incur dependent care costs, you submit a statement with the plan administrator substantiating the cost to receive reimbursement. Dependent care FSAs are generally more advantageous from a tax perspective than taking the tax credit. However, there's no substitute for doing an actual comparison. If you don't incur dependent care expenses that equal or exceed the amount you deposit in the FSA, you forfeit the surplus. Second, once you elect to participate in an FSA and elect the amount withheld, with limited exceptions, you may not change your election.