Does it matter whether I use bank deposits or gross receipts as sales on my federal tax return?

You can see that bank deposits and gross receipts be taken from the same the same information.

The main thing to be concerned with is that the N.M. Taxation & Revenue Dept. compares sales reported to the IRS with total gross receipts (not to be confused with taxable gross receipts) reported on Forms CRS-1. If bank deposits are reported to the IRS, the total will be greater than total gross receipts because deposits include gross receipts tax. The TRD takes this into account when they  determine whether the discrepancy indicates that the business has not reported all of their gross receipts.

Using bank deposits is technically correct because N.M, state law make the seller liable for gross receipts tax. From an accounting standpoint, when a gross receipts report is filed a liability is created; and, when the tax is paid the payment offsets the liability. Consequently, there is not a business deduction on the income tax return.