In addition, people have to be able to financially handle the high-deductible health plan that such accounts are attached to—which means, in 2017, a deductible of at least $1,300 for self-only coverage or $2,600 for family coverage.

Tax advantages for HSAs are pretty substantial. Contributions are tax-deductible, investment growth and interest are tax-exempt and withdrawals aren't taxed as long as they're spent on qualified medical expenditures.

And while contributions to HSAs are limited—individuals can save up to $3,400 annually, while contributions to a family plan can't top $6,750 (those 55 and older can save an additional $1,000)—money that's not spent can be rolled over, and there's no limit on that.

Morningstar reviewed the 10 largest providers of HSAs, looking at them both as spending vehicles to cover current medical costs and as investment vehicles to save for future medical expenses.

But despite the plethora of firms and plans available across the industry, the report concludes that "only one looks compelling for use as a spending vehicle and an investment vehicle, suggesting there is much room for improvement across the industry." That one is The HSA Authority.

The factors Morningstar considered in its evaluation should be on every investor's and employer's list, lest they end up with a plan that doesn't fill their needs.

At the top of the list for HSAs to be used as spending vehicles—used to cover current medical costs—are account maintenance fees, and three out of the 10 scored positively in that area; each offers checking accounts without monthly maintenance fees. They are Alliant Credit Union, SelectAccount and The HSA Authority.

When considering how well HSAs perform as investment vehicles, investment menus are a prime consideration, and Morningstar says there's room for improvement among providers.

"We gave only four plans positive overall assessments for their investment programs," Morningstar says in its report. They are Bank of America, HealthEquity, Optum, and The HSA Authority, and their plans have at least two of the three features mentioned above.

Just four plans— Bank of America, HealthEquity, HSA Bank, and SelectAccount—offer "robust" investment menus, defined as "offering exposure to core asset classes with limited overlap among options."

And when it comes to strong underlying managers, in seven of the nine plans (one declined to provide an investment menu for evaluation), more than half of the investment lineup receives a Morningstar Medal.

But the strongest are BenefitWallet, HealthEquity, Optum, and The HSA Authority.

Plans can come out cheap or expensive on investment fees, with Bank of America, HealthEquity, Optum, and The HSA Authority offering investments for a total cost "meaningfully lower than retail mutual funds."

Then there's performance, with underlying funds in the evaluated plans generally outperforming their peers. But the best are Bank of America, BenefitWallet, HealthEquity, HealthSavings Administrators, Optum and The HSA Authority, which had especially strong risk-adjusted returns compared with their competitors.