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

Bank deposits and gross receipts are taken from the same the same basic information - assuming you deposit all money receive from sales.

Whichever one you choose to report to the IRS, the main thing to be concerned with is that the N.M. Taxation & Revenue Dept. compares sales reported to the IRS with total reported gross receipts (not to be confused with taxable gross receipts). Note: If bank deposits are reported to the IRS, that amount will be greater than total gross receipts because deposits include gross receipts tax. The Taxation & Revenue Dept. takes this discrepancy into account when they determine whether the it indicates that the business has not reported all of their gross receipts.

Comparing bank deposits with GRT reports
Determining reportable gross receipts
I received a GRT audit letter