Filene found that the best predictors of members' choice of auto lender included more intangible aspects of the lender, such as the borrower relationship in members' past auto loans. For instance, members who placed more importance on customer service were far more likely (by 41%) to choose a credit union for their auto loan.

"One of the most interesting findings is the fact that with current loans and future loans, people didn't tend to care much about terms. Often, that's what credit unions lead with," said Ben Rogers, research director at Filene in Madison, Wis.

Indeed, while it's true that customers undoubtedly prefer more attractive loan terms, Filene found that low interest rates, flexible repayment structures and down payment requirements were not useful predictors of members' choice of an auto lender.

This comes at a time when credit unions are providing better rates than commercial banks, Filene said, citing data from the CUNA, Datatrac and the Federal Reserve. Between 1986 and 2009 credit unions' share grew from 13% to 22%, while commercial banks' share fell from 47% to 33%.

When choosing an auto lender, credit union members do not consider the national averages of the interest rates charged by credit unions, commercial banks and finance companies, according to the report. Instead, they take into account the actual rates that ­individual institutions offer to them.

Another notable distinction was a member's age, education or income not having an impact on the choice of lender for an auto loan, Filene discovered.

Meanwhile, members who sought financing, placed more emphasis on customer service, ease of contacting the lender, lender responsiveness, convenience in making payments and ease of the application process.

Rogers said one of the key takeaways for credit unions is to spend more time on how to make the loan process easier. Part of that ease may start with how credit unions actually communicate with their members.

"We were really interested in how members like to be contacted and which marketing channels worked," Rogers explained.

Filene found that 92% of the members surveyed preferred their credit union's website, with email in second place at 81% and direct contact employees at 72%. Far less importance was placed on traditional, less interactive means of communications, including postal mail (51%), statement inserts (39%), and brochures and signs at branches at 32% and 29%, respectively.

Of all the preferred communication channels, social media came in dead last at 16%. Still, when it came to how credit unions marketed auto financing, it wasn't a huge predictor of the type of lender members ultimately chose. 

Members who placed more importance on credit union websites were only somewhat more likely to choose credit unions for their auto loans (79%) than those who considered websites less important (70%), the data showed.