with regard to the why mothers day gets more attention than fathers day is very simple. We live in a gynocentric world, and thats that.
about the primary question I would say this is a night and day conversation. in our society we have condition young men to be as hands on with children as moms esp when first born, I know I was with both of my kids, bottles up all night etc the hole nine yards. I understand this is to assist and this goes back to the whole concept that everything domestic wise is 50/50. personally I believe that things between men and women are NOT meant to be 50/50 I dont think this is how nature built us.( or how god built us)
my take is that from birth to somewhere around preteen the bond is with the mother and she meets the needs of the child after that once preteen its Dads turn! I believe its fathers that turn young boys and girls into Men and Women. mothers get them to a certain point than its fathers who teach them how the world works.
This is just as important for Girls as Boys. as young boys its obvious how the father teaches them but for the young girls the Father shows them how a man should be, whats its like to live with a man hes provides and cares for her... when she goes emo crazy he calms her. but also too he puts her in her place when the behavior is not right, she may have been a princess when she was a toddler but now she is a young woman and she gets NO more free passes.
the lack of a father in this regard is epic and difficult.
fathers love in a totally different way than mothers do, the old psychological order was
Father loves Mom unconditionally....Mom Loves father conditionally
Mother loves Children Unconditionally ....Father Loves Children Conditionally
I believe this is not far form the truth in general terms. Of course there are always those unicorns out there where this doesn't apply.