Can she take a sword and go toe to toe with a dude? Hell freaking no.
Unless she's a freak of nature or he's a shrimp, he's going to gut her like a fish.
I'll use myself as an example.
I'm 5'6" and weigh about 120. Average.
When I was 17 a guy beat the shit out of me. Not slapped me around, not hit me. Put me in the hospital. He was 5'8" and weighed about 155. It wasn't like I just sat there and took it. I fought. I kicked, I punched. I scratched, bit, pulled hair. Did everything I could think of. Didn't matter.
Now there's a point to be made here - after all, athletes are split by gender because the most devoted female athletes can't match up to the most devoted male athletes.
But overall, I disagree with this. Any experienced martial arts instructor will say that if you weigh 120 lbs, you can hit with at least
the force of 120 lbs. We don't live in a warrior's world any more. Outside actual military conflicts (which are rare) and perhaps SWAT teams and the gang life, most people never see any violence in their lives. Your average person 1000 years ago will likely have spent as much time in military training as we do today in schooling and college.
There is a stark difference between someone who practices kickboxing on weekends and someone who does military training on weekdays for 10 years. In real conflicts, you try to punch the throat or gouge your opponent's eyes out. None of this is trained in most modern martial arts. You don't need a lot of strength to take out someone's eyes. And unless you're parrying blows (which is actually quite dumb), you don't need a lot of strength to jab a knife anywhere inside a person.
Of course, your average man today can beat up an average woman easily. But it's like saying, "Hey, my IQ is 100. A man's IQ is 130. I should just skip university and get a menial labor job now because I'm going to get nowhere with my disadvantage."
For a real look at the situation, look at the police force of any country, not the military. Police face real, dangerous conflicts all the time. There are plenty of policewomen out on the streets. They're not all guns either, any real police officer needs to be prepared to go into a conflict unarmed. I've heard stories of a 40+ year old homeless, undernourished (but mentally ill) woman throwing a trained police officer twice her size and biting his face off. I've also heard stories of country girls who can easily lift things their own weight, because they do it every day.
Take a big guy, trained in any martial arts... more so the type which trains people to 'disarm people wielding knives'. Find a female friend, average sized. Give her a marker, pretend it's a knife. Tell her that the big guy is trying to take away and kill someone under her care (like a little brother or son). Half the time, the guy will have marker marks on his throat and face. Give the guy a marker to even things up and she still stands a good chance, because the martial arts conditioning will slow down the trained person.
Size and strength do matter. Nobody, male nor female, should be using grapples, blocks, and locks with a 300 lb ex-convict. You shouldn't even be trying to hit them with blunt weapons. I would say the female still does better in such a situation, because she's trained herself to never let her opponent use their strength against her.