The Consumer Federation of America said yesterday that credit unions offer the best deal on basic financial services to customers.

That assertion was based on information about credit unions gathered by a trade association for credit unions, the Credit Union National Association. It was also based on a survey of charges related to checking accounts, which are offered by only 30 percent of all credit unions nationwide and which account for less than 10 percent of credit union deposits.

The CFA contrasted the information favorable to credit unions with information it gathered earlier this year on a much smaller number of banks, and joined the CUNA, which is one of its members, yesterday in urging consumers to use credit unions for their basic financial services.

A study released by the two groups concluded that credit unions rarely charge for maintaining an interest-bearing checking account, obtaining travelers checks or cashing Social Security checks. The study comes at a time when the nation's credit unions are fighting to keep their federal tax exemption.

"If banks had the same tax advantages that credit unions enjoy, you would see a much closer parity between their costs and prices to consumers," said Kirk G. Willson, spokesman of the American Bankers Association.

The Reagan administration's tax overhaul proposals would strip the tax-exempt status of credit unions, a move being resisted by credit union officials.

The survey concluded that 75 percent of credit unions offering interest-earning checking levy no routine charges such as monthly and per-check fees, while only 5 percent of banks and savings and loan associations can make this claim for equivalent accounts.

Fifteen percent of credit unions place clearance holds on local checks, compared with 82 percent of banks and S&Ls surveyed, the credit union study said.