It seems that, kind of like our world, men seem to be more in charge, though there is the Old One, who is a matriarch leader of a herd (though perhaps she had a mate that was, in fact, the leader of the herd, but he passed on, leaving her as the leader.)
I mean, though they all are supposed to control the leadership together in the Great Valley, it seems that Topps and Grandpa Longneck hold quite a bit of sway in the decisions.
Also, other than the Old One, we've never seen a female lead a herd. It's always the male Spiketail leader (Tippy's herd), Bron (Bron's herd), and possibly Grandpa Longneck and Topps as the main de facto leaders of the Combined Herd in the Great Valley.
Also, the fact that Grandma Longneck uses the word "his" instead of his/her when mentioning about the Big Longneck Test and who takes it also seems to back the patriarchy theory. Perhaps it was just because Littlefoot is male, but perhaps it is only available to males and hence Ali wouldn't be allowed to take it. (Give it someday to a child of hers, yes, but not take it.)