Leadership roles would be more occupied by men than women, but I think the sexes would survive at similar rates.
I think most post-apocalyptic tribes would be run by dictators, either benevolent (Rick, Herschel, even the governor to some extent) or non. Women are just as capable of being dictators, but I do think it's likely that more men than women would assume such rules, since they'd likely be filled by either the toughest/best armed folks, or people with direct leadership experience over people performing physical tasks (military, firefighters, gang members), and currently those roles are dominated by males. I see no difference in capability between the sexes, but prior experience would be a major factor.
On the other hand, I wouldn't expect much of a difference re: survival rates* between sexes, as whether or not somebody initially survives is probably more a result of luck than anything, and whether or not a person continues to survive would be a result of a whole host of factors like location, cunning, resourcefulness, cooperative ability, and so on. Physical toughness is included, but is not more important than the other factors.
*i think children under 10 would be a major major problem. While potentially a psychological boon, they're noisy, unsanitary, and are resource vacuums. survival rates for those supporting young children would likely be much lower, and it's possible that more women than men would attempt to support children, based purely on initial proximity.