Private exchanges generally have been more popular than their public counterparts among insurers and employers alike, but they may not be quite so good for consumers, according to new research.

HealthPocket, a website that compares and ranks health plans, found that two of the leading online private exchanges — Extend Health, described as the "largest private Medicare exchange," and eHealth, described as the "largest private health insurance exchange for individuals and families" — offer fewer options for consumers to consider compared to government plan finders.

Though gaps were also found in the government options, on average, only 41 percent of Medicare Advantage plans and 49 percent of Medicare Part D plans were found in the private exchanges compared to the federally-run medicare.gov.