But satisfaction levels trended up in most years of the survey among CDHP enrollees and down among traditional-plan enrollees.

Still, consumers don't have an entirely rosy view of their consumer-driven health plans.

Enrollees in CDHPs and HDHPs were much more likely to report they weren't too or not at all satisfied with their health plan, presumably because of higher out-of-pocket costs.

But those dissatisfaction levels also have trended downward in most years of the survey, said Paul Fronstin, director of EBRI's health research and education program, and author of the report.

“Satisfaction rates for out-of-pocket costs were much higher among those with traditional coverage than among those with either an HDHP or CDHP, though regardless of plan type, satisfaction with out-of-pocket costs was consistently low,” Fronstin said. “However, satisfaction rates do appear to be trending upward for those with a CDHP.”

Consumer-driven health plans—and their associated products, such as health savings accounts—are becoming more popular among both employers and employees.

According to analysis from the American Association of Preferred Provider Organizations, enrollment in consumer-directed health plans grew by 19 percent in 2012, increasing from 33 million in 2011 to 39 million last year.

Meanwhile, despite the fact that satisfaction is on the rise for CDHPs, EBRI researchers pointed out that those in a traditional health plan were more likely to recommend their plan to a friend or family member than those individuals in a CDHP or an HDHP plan. Fronstein said that finding is likely driven by out-of-pocket spending than by quality or access to care.