I really don't like the idea of a battle of the sexes. I think both sexes would have lost ground in that case. Outside of the stripper polls, I have seen where many women have started tightening up and shortening their attire on a whole scale in order to appease or attract men. On the other hand I've seen where many men have become slaves to porn, sex and other stuff directly related to women. Images of women are used to sell men things such cars, beer, clothes, various sorts of entertainment and vacation spots. So really, I don't know who is winning.
I think the problem with "the battle of the sexes" is that it's similar to asking the question "which is better - an apple or an orange?" We are wired differently and on average have different strengths and weaknesses. We are designed to compliment each other, not "win" or "beat" each other in some competition to see which is better. It would be pretty boring if we we all the same and our worth measured on just a few dimensions. Surely we've evolved past that?
No, I agree with you on that front parks. But, there still remains a battle of sorts, perhaps it's not so much each sex pitted against the other, but certainly against those who objectify and those who are objectified.