I must admit, I also find it sexy when the good girl gives her all, but is still vanquished by a nefarious foe. I like your basic scenario, and I honestly don't think it needs to go to a variety of locales or titanic deeds to be dramatic, though if you're inclined to go that route it can work that way also.
My general thought is that Miss America will have had a longer time to grow comfortable with her powers, so she'd be likely to take control early and come very, very close to finishing Lady K. off. However, Lady K was a spy first, and likely had some sort of combat training as part of her background. As the fight progresses, those reflexes adjust themselves to her current capabilities. Once that happens, we'd see a shift in the dynamic as she first defends against, then reverses the huge advantage that Miss A. had created. Miss America has never had to battle someone of comparable power, and once Lady Kamikaze has gained her composure it would gradually become apparent that she's a superior fighter. This will come as a shock to the patriotic beauty, further throwing her off her own game.
Once the American heroine is on the defensive, Lady K. would focus on slowly but surely crushing her physically and mentally. Rather than just working to secure a 'win' as Miss America would be, her personal grudge would lead her to relentlessly grind down the blonde until she broke her spirit as well as her body. This wouldn't be easy, of course. Miss America is a strong woman, and not just because of her powers... but everyone has a breaking point. IMO the crux of the story would be finding it.
-JM
