I have to disagree here. A matrilineal society, as I stated in my previous comment, does in fact often give women more access to familial resources, as these are often given to women to be managed or inherited from women, by women.

Hence often piously called matriarchal, as in "The Afro American family tends to be matriarchal"

In practice, "matrilineal" societies are often societies where no one knows, or much cares, who the father is. As our society becomes increasingly like this, the proposition that women benefit from this arrangement starts to smell funny. Men in a matrilineal society contribute substantially less to the support of women and children, and often the relationship is that between a pimp and his bitches: the women (plural) support the man (singular). The male contribution is frequently large and negative.