Supergirl isn't less powerful because she's a woman, she's less powerful because she's a girl.
Superman is older.
That's why Mon-El was stronger than Superboy and Supergirl but weaker than Superman. Mon-El was physically older than his brother and cousin.
Not only is Superman older than Supergirl, he's got five years more experience with is powers than she does, and got used to them gradually.
By the way, I definitely see what you mean by "postmodern take on the 70s". I get that vibe as well, and if this is a second Bronze Age, I think it's a pretty good one.
That argument works for the pre-Crisis versions of the characters because there wasn't a charging element to their powers. When DC reintroduced Kara Zor-El, they had her soaking up solar radiation for 25-30 years while in suspended animation never once exerting that massive amount of energy. Superman had been constantly exerting and recharging his energy levels throughout that time.
We've seen what happens to Superman when he absorbs a massive amount of solar energy; he gets stronger, faster, etc. So, it's logical that his cousin would be stronger than he is initially until she exerted that surplus energy and her powers tapered off to a normal level.
Also, experience only goes so far. At a certain level, it wouldn't matter how experienced you were if your opponent was stronger, faster, etc. This occurred when the Post-Crisis Superman first encountered Daxamites (and before they had a charging element added to their powers): Supes was manhandled by a couple of Daxamite scientists who had just gotten their powers, struggled with the rookie Lar Gand, and failed to defeat Dev-Em in hand to hand combat.