People with Obamacare plans—particularly those who re-enrolled this year—were significantly more satisfied with their experience signing up for health insurance than customers were last year, according to a new report. Obamacare customers nationally also tended to be more satisfied with their plans bought in 2014 than people who primarily have traditional job-based health coverage—the majority of those with insurance—the study by the J.D. Power market research company found. Read More2 states' surprise Obamacare success

And those customers from last year were as happy with their coverage as other people who had multiple choices when it came to buying plans outside Obamacare markets from insurers or brokers, according to the J.D. Power report, which was released Thursday. "Cost is the most influential attribute driving satisfaction among [Obamacare] plan enrollees," the report said.

Ariel Fernandez, left, sits with Noel Nogues, an insurance advisor with UniVista Insurance, as he signs up for health insurance under the Affordable Care Act in Miami. Getty Images

Rick Johnson, director of the health-care practice at J.D. Power, said that Obamacare "marketplace shoppers are very cost-sensitive." "Unlike many traditional health-plan members, who are often tied to a single employer benefit offering, marketplace members have the option to switch plans annually, allowing them to shop for either the most affordable or the most valuable plan." However, the study, which questioned 3,037 new enrollees and returning enrollees, found that Obamacare customers' satisfaction with their plans tended to vary depending on the kind of government exchange they used to buy coverage. People most satisfied with their plans bought them on HealthCare.gov, the federally run marketplace. HealthCare.gov customers tended to be more satisfied with their plans if their state had partnered with the federal government to conduct enrollment, as opposed to if they were states that opted out of running their own exchanges. Read MorePatient costs rise, ability to pay falls

Customers overall who used one of the 14 individual exchanges run by a state or the District of Columbia had the lowest satisfaction with their plans of any kind of Obamacare customer. But notably, HealthCare.gov scored dead last among federal government agencies in the U.S. Customers Experience Index report issued by earlier this week. And federal government agencies, as a rule, tend to score much lower on Forrester's index than any of the other 17 industry sectors examined. A spokesman for the Centers for Medicare and Medicaid Services, which operates HealthCare.gov, declined to comment on either the J.D. Power or Forrester Research report.