Really, I have a question about fixies on hills, but I'll use another "girl race" to frame it.

As I pedaled along on a level stretch, at about 90% of my full capability, she passed me easily.
Easily.
A friendly "Hi, passing," and she pulled away, no body fat, powerful legs, and a $6000 bike.
I bumped it up to 95% but soon saw the pointlessness of it.

Ahead lay a hill, perhaps the most severe hill in Bend that bicyclists normally travel.
I thought she would get to the top before I even got to the bottom.
However, as I rounded the curve approaching the hill I could see her ahead of me, out of the saddle, about a quarter of the way up the hill.
She looked comfortable and in her element.

As I hit the bottom of the hill I got out of the saddle and continued at the same pace.
To my surprise, I quickly closed on her and by halfway up the hill passed her at twice her speed.
Oh no!
The dog that caught the car.
Now what would I do?

At about 3/4 of the way up the hill not enough oxygen existed on the entire planet.
I can max out a lung inspirometer at 5000cc's, but my lungs felt puny.
I saw myself as a drowning man, sinking deeper and deeper with each stroke and each breath, but I couldn't stop.
I had to beat THE GIRL.

Yes, I know that if I'd said "tag" as I passed it might have turned out different.
I didn't give her an invitation to the race and it probably didn't even occur to her.
Perhaps I caught her daydreaming or cooling down after a 30 mile training ride.
It doesn't matter.
In my frightened, insecure little male mind I knew I had passed her on the hill and maintained my pace to very top (even though I scared myself with oxygen deficit).

Which brings us to the question.
I have my own answer, but I'd like to here what other people say.

Why, on the average, do fixie riders do better on most hills than do roadies?