The site did not reveal what percentage of banks offered free checking if a customer started using e-statements or direct deposit.

Bankrate said the percentage of both credit unions and banks offering standalone free checking has fallen since 2010, with 6% fewer credit unions (78% in 2010 to 72% in 2014) offering the no-charge accounts, and 27% fewer banks doing so (65% in 2010 to 38% in 2014).

Greg McBride, Bankrate's chief financial analyst, attributed most of the disparity to the regulatory changes in debit card interchange.

The Durbin amendment to the Dodd-Frank Act capped debit card interchange for financial institutions of with over $10 billion in assets. Significantly, all four credit unions with more than $10 billion in assets, which have had their interchange capped by the law, also participated in the survey.

Debit card interchange helped subsidize the costs of checking accounts that carried debit cards, McBride explained, but with the cap, those accounts began to lose a bit of money and have become harder to maintain as fee-free.

But he also suggested that getting more consumers to try electronic statement delivery and direct deposit, both of which help cut checking account costs, was also driving some of the shift.

“I would say that it's definitely a mix of things, but the biggest is likely the difference in interchange for the bigger banks,” McBride said. He observed that community banks, which like most credit unions have fewer than $10 billion in assets and are therefore exempt from the debit cap, had also not reported as steep a drop in free checking offers as the big banks.

Consumers also got a better deal from credit union checking accounts than bank checking accounts in other ways. For example, bouncing a check at one of the 50 largest credit unions will cost a account holder $26.96, whereas at a bank a bounced check will cost an average of $32.20.

Bankrate also reported 30% of the 50 largest credit unions don't charge their members for using another financial institution's ATM, or provide at least one free withdrawal per week from another institution's ATM. But almost all of the largest credit unions (96%) charge non-members for using their ATMs, Bankrate reported.