(This is an image-intensive post. If it's too much, moderators are [obsiuvly] absolutely free to delete any pictures

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I have to put the final word in the "Supergirl vs Superman" matter. In the most scientific way.
First, I, ehm, tracked down a copy of the DC Heros RPG.
This rule book (and the supplemental books) was written with direct input from the DC Comics editorial staff (for example Alan Moore collaborated with the Watchmen sourcebook)
Then I used the official stats of the (precrisis) Superman and Supergirl
Superman:





Supergirl:

As you can see, some Superman stats, like Strength, are superior to her cousin's ones. But, like every RPG player knows, a fight result isn't only the mathematical comparison between some numbers (well, like the real life).
First of all, it was clear that Superman wasn't completely thinking straight. So a Master would low his Dexterity and Intelligence stats of some points (Dexterity is useful to dodge attacks, remember how in the episodes Kara dodged more punches than Kal).
Then, a Master would limit how many strength points Superman can use. Remember, we are talking about
Superman. Throughout his life he has always limited, consciously or unconsciously, how much force to use against a living being. And they were fighting in a populated city.
Then there are the Hero Points. Kara can burn all her Hero Points to momentarily increase her fighting stats. Exactly like when in comics a hero burns his/her last reserves for a last attack.
In addition, obviously, sheer luck must be considered (the results of dices rolls). With a little luck Supergirl can obtain some Critical Blow and/or Devastating Attack (there are special rules for them).
Considering all of these elements, could Supergirl beat Superman? Absolutely yes. Would it be difficult? Obviously yes (and it wasn't a piece of cake in the episode too). And probably the fight would leave Supergirl with her Resistance Points almost completely depleted (and again, in the episode she passed out).
'nuff said!