When Supergirl first arrived from her extinguished home of Argo City, her body quickly acclimated to the yellow solar energy and reduced gravity of Earth-One, producing within her power levels approaching those of her cousin Kal-El. Simaltaneously but a universe away, her counterpart Power Girl had herself entered Earth-Two's atmosphere following her disembarking of her celestrial home, the Symbioship, to find herself having possessed an above average physique, though her powers would develop overtime as had her cousin Kal-L. Why the difference? Unlike those residing on Krypton-One, the residents of Krypton-Two had superstrong abilities allowing them to adapt to the crushing graviational pull of their world, although conversely on Earth-Two they were limited by that phyiscal manifestation of their adaptation. Meanwhile, the Kryptonians who lived on Earth-One could absorb stellar radiation which allowed their abilities to exceed those of their dopplegangers.
So when Power Girl first appeared, her superstrength and speed didn't approach those of Supergirl, and unlike her cosmic twin she couldn't fly, being confinded to leaping great distances. Eventually, Power Girl would develop comparable levels to Supergirl, although she like Kal-L could not match Kal-El and Kara in a one-on-one confrontation. Unless, of course, it was through skill and particularly tenacity, which Power Girl would possess in abundance over Supergirl given her willpower and longer training period under the tutelage of her cousin.
In the end, though, this confrontation would come down to who was more "super", and we know whom that would be.