"Employees who work for a female manager are six percentage points more engaged, on average, than those who work for a male manager. Female employees who work for a female manager are the most engaged; male employees who report to a male manager are the least engaged," Gallup's report says.

However, simply replacing male managers with women and hiring more women won't solve America's productivity dilemma, Gallup said. Because far too few workers of either gender are engaged in their jobs.

"In the U.S., working women have the engagement edge. But there is an important caveat: While female employees have higher levels of engagement than male employees, only slightly more than one-third of women are engaged at work," the report says.

According to the Gallup poll, men just seem less happy overall on the job. Gallup asked men and women a series of specific questions designed to elicit engagement information, and women outshone men on 11 of 12.

Biggest gaps were found when they were asked to say yes or no to the following:

• In the last seven days, I have received recognition or praise for doing good work. (+10 for women)

• There is someone at work who encourages my development. (+8 for women)

• The mission or purpose of my company makes me feel my job is important. (+6 for women)

• At work, I have the opportunity to do what I do best every day. (+6 for women)

The only statement where the genders are in a dead heat: "My opinion counts at work." Men did not outscore women on any statements.

The female manager phenomenon is something employers need to take seriously, Gallup says. The fact "female managers are more successful than their male counterparts at figuring out how to put the [engagement] pieces together" demands further study. 

"Female managers surpass their male counterparts in cultivating potential in others and helping define a bright future for their employees. This does not mean female managers are more likely than male managers to promote their associates. But it could signify that women are more apt than men are to find stimulating tasks that challenge their employees, thus ensuring that associates develop in their current roles and beyond," the report says.

"Overall, female managers eclipse their male counterparts at setting basic expectations for their employees, building relationships with their employees, encouraging a positive team environment and providing employees with opportunities to develop in their careers."