Hah, fascinating and very complex question (and I love to dissect things like this!!)
According to experts:
The mother plays a more prominent role during the first 3 or 4 years of life teaching the infant valuable lessons of love & patience. (Doesn't mean that Dad can't tho!)
After that, the child will begin to primarily focus on the same sex parent (they learn how to be a lady for Mum, or how to be a man from Dad).
During the early teens, the child will then shift primary focus onto a mentor - a role model of the same sex (a grandparent, an aunt or uncle, a "cool" teacher, neighbour or boss can fill this role). Children who don't find this relationship (especially boys) will rely on peers...which is a case of the blind leading the blind - you're just asking for trouble!
I personally believe that both parents are equally important BUT they are important for different reasons.
It could be compared to they way we love our children - we love them all equally but we treat them slightly differently according to their individual needs and characters. And so it is with parents, we need them both but to provide different roles.
PS - Apologies to single parent families...admittedly there are definitely cases where the child is better off without a parent's influence. Raising a well adjusted child is absolutely possible in single parent families and I admire the strength and determination of any parent who is required to fill the role of both mother and father. Good luck to ya =)