The 2015 study to which this question seems to refer, titled The State of the American Manager: Analytics and Advice for Leaders, suggested that female managers likely surpass their male counterparts in cultivating potential in others and helping define a bright future for employees. (This does not mean they are more likely to promote their associates; but, it could signify that women are better than men at finding tasks that stimulate staff, thus ensuring associates develop within their current roles and beyond.) Further, female managers are more inclined than men to check on the progress of employees. The study also discovered that female managers themselves are more engaged at work than their male counterparts. To suggest that this can be true in most circumstances would require a leap of faith.
To the extent that women leaders have greater empathy and perceive needs, concerns and problems of others, members of their teams are also more likely to identify with the goals of the team and are thus motivated to work for common goals.
Some recent research that I have been seeing describes specific leadership interactions that seem to predict engaged teams. These interactions include, for example: active listening, individualized encouragement, facilitating respectful team interactions, and ensuring that all voices are heard. The empirical work is not yet published and is based upon the complexity leadership capabilities approach described in the attached theory article.
It would seem that an interesting study would test whether women do these things more than men. If so, it is a simple step to conclude that women managers would have more engaged teams.
Note, however, that the implication of the complexity approach is not that women managers lead teams that are more engaged. It is that women managers are more likely to engage in leadership interactions that engender more engaged teams. Anyone can learn to facilitate the requisite leadership interactions.
Article Towards operationalizing complexity leadership: How generati...
Could there be something also around women as opposed to men being comfortable with active listening? This I recognise is a ridiculously sexist comment for today, but in my experience it holds true and is an important part of, as Eva posted, empathy.
Women managers generally resort to management through transformation, as opposed to men who generally manage through transaction. By nature, women are more caring and sharing, therefore possess the skill of forming cohesive and engaged teams through transparency, communication, ethics and providing transformational leadership.