They're both true, though. Expectations of decent parenting are lower: just taking both my children to the park gets 'wow, that must be a handful' comments that my wife doesn't get. At the same time, I'm not assumed to be a competent caregiver, and am excluded from some of the social/mutual support side of parenting as it's in practice mums only.

GP is correct; these are in many ways two sides of the same sexist coin.