I think it would be easier in many ways, but not all. But, I also believe the reverse is true. Men would have an easier time being a woman in many ways but not all.
The reason I think this doesn't have to do with things being "easier" for one sex over the other but because the skillsets each gender is socialized with, and more importantly, socialized against, make certain things more difficult for one gender over the other. Frankly, this is common sense.
To you example, I agree with the woman about going out and having so much random sex. She probably would/could, as far as the skillsets required to get someone to have sex with you goes. She's not goinf to have the difficulties with this that men do. Not by a long shot.
But here's the thing, and where I potentially disagree with her. If you suddenly get transformed I to a man, is that just biological, or completely? Psychologically? experience wise? All those things.
Because she's assuming that she gets to keep her woman skillset in a man body but be relieved of the burden of sexual shame women have to carry.
And that may be fair. One is individual. The other is how you're treated based on what you look like or who you are.
You, on the other hand, are assuming that if she is turned into a man she will automatically have all the same difficulties as a man, based on one woman's experience.
I think there will be a learning curve, but I think more people would do better than what one example suggests. Particularly someone who was struggling with severe mental health issues that would impact her ability to function, regardless of what gender she was presenting as.
Her experiment was interesting, but I think men put too much focus on a whole lot of nothing in it.