The findings are based on an analysis of the 2010 Well-Being Module of the American Time Use Survey, the government's detailed look at how people spend their time. The module is used to judge how people feel during the activities they record during the day.
The Pew analysis took a narrow look at 18- to 64-year-olds with children under 18 living in the household.
They found that parents also are happier when they are with their kids. Parents rated themselves as "very happy" in 35 percent of their child care activities, versus 19 percent of their work-related activities.
(Read more: Here's a career tip: Leave Mom and Dad at home)
Wang said it was especially interesting to find how little work time appeared to be very rewarding to parents, and to see that that figure was not much different between moms and dads.
"Dads are just like moms in feeling that their time in their paid work is not as meaningful as their time in child care," Wang said.
One big difference is who's more exhausted by juggling it all.
Moms were more likely than dads to report that all the activities Pew looked at—paid work, child care, housework and even leisure activities—made them very tired. The gap was quite large for child care, with moms reporting that it was very tiring 15 percent of the time, compared with 6 percent of the time for dads.
(Read more: Why more parents are choosing 'one and done')
Wang said that might have something to do with what kind of child care they do.
Dads are spending a lot more time with their kids than a generation ago, but on average moms are still doing much more child care than dads.
The Pew analysis also found that mother and fathers spend about equal time playing games and sports with the kids. But moms spend a lot more time doing things like changing diapers, dropping kids off at school and helping out with homework.
"That could explain why mothers are more tired," Wang said.
—By CNBC's Allison Linn. Follow her on Twitter
@allisondlinn and Google or send her an email.