This is a very touchy topic. All parents are different and all children are different. Each parent has a different style of raising kids and this difference may even happen within families between the mother and the father. the children, though, will bond hopefully with both, but most likely with one or the other. If the parent is nice, attentive, supportive, and plays with the child, then the bond between then is (1) more likely to happen and (2) more likely to be very strong. If the child is neglected, the child will most likely be standoffish.
It may be true that everyone has their own style of child-rearing, but I think two parents of the same child generally agree on a method of raising the child. After all, a disagreement about this among parents may in and of itself detract from the formation of a secure attachment.