I watched the video but stopped when it seemed the whole thing was just going to be ways in which men and women aren't equal. I got bored with it because of course I already know that, and pretty much everyone knows that and accepts that statistics in all sorts of areas aren't equal for men and women. Whoever made that video seems to be defending a point that isn't under any particular contention. I'm not sure how much of that video you'd like debated in this thread, but I'll give my thoughts.
Men and women aren't behaviourally identical - any sane person accepts these statistical differences. What is under contention is how much these observed behavioural differences are due to biological, innate differences between genders, and how much is due to environmental and cultural influences.
The video makes a number of dubious points as well. For example, its implicit assumption that female 'circumcision' is equivalent to male circumcision, and what seemed to be the idea that women should be treated more harshly by the justice system in order to make up for the deficit in crimes committed by women and balance execution statistics, which sounds bananas so maybe I have misunderstood.
The introduction to the video also discounted (or refused to acknowledge) reasons that might explain differences in men and women's employment over history (e.g. social expectations of gender roles, prejudice, etc.) and asserted that the reason there isn't equal employment must be because women are 'not equal', which is vacuous at best and misleading at worst, since the same thing could have been said in the past (and still somewhat today) about black people: "why are there no black presidents or judges, etc.? Because they're not equal to white people." That's a completely absurd way to phrase it when yes, there are physiological differences (and possibly statistical psychological ones too - I don't know), but of course we know that the reason there weren't black presidents was because people who held power were prejudiced against them. The author of the video just glosses over all this stuff and says it's because women "aren't equal", as if that answers anyone's questions or is an intelligent input into current debate.
Liberals and feminists and so on don't believe men and women are behaviourally identical, they believe that men and women are deserving of equal opportunities. The means of securing that is what is disagreed upon (e.g. equal representation in the workplace, incentive schemes, etc.).
So, would equal outcomes be terrible for the average woman? I think it completely depends on what is meant by 'equal outcomes'. If it means people are effectively blinded to gender and people are more-or-less rewarded based on merit, I don't think it'd be bad at all. At present, there are ways in which the average woman might have it easier than the average man, and vice versa, but all those points in the video notwithstanding, I think women probably have a tougher time than men. I just have to ask myself: if I was killed and got to be born again, would I want to be born a woman? No way. That I think says it all.