Supergirl vs. Superman
I've been reading the collections of the Supergirl comics, issues 1-9 so far. They clearly imply Supergirl, at least for the time being, seems more powerful than Superman. He admits it might be because she was exposed to intense solar radiation from technology in her ship all the way to Earth but it might also be because he has learned to hold back and she hasn't. But those are character claims, word balloons, not feats.
Granted she has shown nowhere near the strength feats he has but the feats she has that I've seen are:
Flies faster than he can and he cannot catch her.
Synthetic kryptonite has no affect on her although it apparently has some weakening effect on him.
Stands up to attacks that hurt him more than they hurt her. Hence, more 'invulnerable'.
Fights opponents such as Blackrock that beat Superman almost easily and then she steps in and beats them almost easily.
Blackrock: "Aghhh! You... You're stronger than he is!"
This and equivalent statements are made again and again.
I don't know what's happened since issue 9 as I only buy Supergirl when the collections come out and I haven't read volume 3 (issues 10-19) yet or other issues beyond that.
For the time being, based on what we've seen so far, is it fair to assume that, until they establish otherwise, she is more powerful? Does she beat him in a fight?