While consumer-driven or high deductible health plans have increased dramatically in recent years, people who have them aren't necessarily very happy with them. Those who are covered by traditional plans are far more satisfied with their insurance than those who have one of the newer types of policies.

But a poll from the Employee Benefit Research Institute, conducted in 2014 but published last week, shows that the popularity gap between the two types of insurance has narrowed over the past decade, with more workers expressing satisfaction with newer types of plans.

While 61 percent of those enrolled in traditional plans said they were satisfied or extremely satisfied with their coverage, only 46 percent of CDHP enrollees said the same. Those covered by HDHPs were the least happy with their plans; only 37 percent expressed satisfaction with their policy.