Forgive me when I say do not believe this is a fair question. As parents, (and I speak with the traditional male and female partners in mind) I believe the husband and wife fight together to help their children learn and progress in life. Of course, the children may have their own preference according to which parent they get along with better, but there should still be a balance between the parents. In this day and age, and I know I can not be alone on this opinion, I feel that people make too many seemingly harmless jokes about men running away the moment they learn their mistress, girlfriend or wife is pregnant with their child. I know that popular reaction also causes many people to lean toward the mother for the question "Who tends to love their children more?"
Still, there are plenty of people that will lean toward fathers because they take them to do things that are seen as peaceful or against the modern world, such as fishing, hunting, or some other activity. Not to mention we have proven time and time again that mothers run away, too. Or they abuse their kids, too. Or anything else, too.
Because technology has provided a way for everyone's opinions to be heard and questions to be asked, we have been seeing more and more complaints about parents. They are dramatic, unfair, we hate them. They are hypocrites, old, and never do anything right. If we began to show more respect for our mothers, who often take us by the hand and teach us how to stand up for ourselves, to believe and have faith in what seems impossible, and our fathers, who pat us on the back, tease us and teach us to be strong, the human race would be infinitely stronger.
But as to answer the oringinal question, this is one of those things that must be perfect and have balance, without being perfect. Parents are who they are, and they can not protect us from papercuts and they can't read our minds. They are unperfect, which makes them relatable and us more likely to become amazing parents, too. But both the man and woman must be there, loving their children with all their hearts, with that complete perfection in them and the total balance between them.
I speak without handicapped parent(s), sick parent (s), or other tragedies in mind. But this is a paradox. Think about it.