Related: 3 HSA facts employees should know

The average employer contribution to an HSA is $474 for a single employee (down 3.5 percent from 2015 and 17.6 percent from five years ago) and $801 for a family (down 9.2 percent from last year and 13.7 percent from five years ago).

For an HRA, the average employer contribution is $1,810 for a single employee and $3,545 for a family, up approximately 2 percent from 2015.

"HRA plans tend to have higher deductibles so employers tend to contribute more to the HRA than an HSA, especially since HRA contributions are not a guaranteed 'spend' by the employer and are only paid out if there is a claim," the authors wrote.

Overall, 35.1 percent of all plans offer an HSA or HRA, which is up from 34 percent in 2015, a 3.2 percent increase.

The study included a comparison of the two plan types by Bob Bentley, manager, underwriting and analytics at Albers & Company, Inc., a UBA partner firm:

With HSAs, the employee owns the account and can take it when changing jobs. HSA contributions can be made by the employer or employee, subject to a maximum contribution established by the government. The plans have a "triple tax advantage" – funds go in tax-free, accounts grow tax-free, and withdrawals are tax-free as long as they are for qualified expenses under IRS rules. Funds in HSAs may accumulate for years and be used during retirement. An HSA must be paired with an IRS qualified high-deductible health plan (QHDHP) – and not just any plan with a deductible.

With HRAs, only an employer can contribute — employees cannot contribute. The employer controls the cash until a claim is filed by the employee for reimbursement. HRA contributions are tax deductible to the employer and tax-free to the employee. To comply with the Affordable Care Act, an HRA must be combined with a group medical insurance plan that meets ACA requirements.

Related: 3 HSA facts employers need to know

The advantages of HSAs are: costs are more predictable as they are not related to actual expenses, which can vary from year to year; contributions may also be spread out through the year to improve cash flow. Employees become better consumers since there is an incentive to not spend the money and let it accumulate. This can result in an immediate reduction in claims costs for a self-funded plan. HSAs can be set up with fewer administration

costs; usually no administrator is needed, and no ERISA summary plan description (SPD) is needed. The employer is not held responsible by the IRS for ensuring that the employee is eligible and that the contribution maximums are not exceeded.

The disadvantages of HSAs are: employees cannot participate if also covered under a non-qualified health plan, which includes Tricare, Medicare, or even a spouse's flexible spending account. Employees accustomed to copays for office visits or prescriptions may be unhappy with the benefits of the QHDHP.

IRS rules can be confusing; IRS penalties may apply if the employee is ineligible for a contribution or other mistakes are made, which might intimidate employees. Employees may forgo treatment to avoid spending their HSA balance, or if they have no HSA funds available.

The advantages of HRAs are: the employer has more control and flexibility in the design of the HRA and the health plan does not need to be HSA-qualified. The employer can set up the HRA as "use it or lose it" each year, thus reducing funding costs. An HRA is compatible with a flexible spending account (not just a limited-purpose FSA).

Related: 9 top FAQs about HSAs, FSAs, and HRAs

Depending on the employer group, HRAs can sometimes be less confusing for employees, particularly if the plan design is simple. Funds revert to the employer when an employee leaves, which might increase employee retention.

The disadvantages of HRAs are: self-employed individuals cannot participate in HRA funding. There is little or no incentive for employees to control utilization since funds may not accumulate from year to year. More administration may be necessary – HRAs are subject to ERISA and COBRA laws. HRAs could raise HIPAA privacy concerns and create the need for policies and testing.