When children are concerned is it better to live with a husband/wife or baby-mama, or baby-daddy?

Disclaimer This question is in the spirit of a child who shares the DNA of both parents. Therefore, it doesn’t directly include those in same-sex marriages because biology doesn’t support it, sorry I did not create the reproduction method. Also, live with does not include marriage for the baby-mama, or baby-daddy, where unwed cohabitation is the controlling situation. Just so we know the foundation less some quip or flippant comment be made out of context.

Are children better off with a spouse you are married to, or one you just live with, even if for the children sake when you do not have love or lost love for the other person; but they just happen to be the other parent. Your interaction with your son, or daughter would be better and smoother, or would there be more parenting conflict if you were not officially united to your spouse? Would you expect that if you were just living together because of the common thread; the child, it would be harder to come together on raising the child? If you were the baby-daddy would you think you would have a harder time pushing your agenda than if you were the baby-mamma?