Man of Steel showed how a fight would have gone with much more plausibility.
Superman fought Faora-Ul and her superiority in hand to hand combat was plain to see. He couldnt trade blows with her and hope to win so he resorted to brute forcing his way through their fight; charging into her like a speeding car using his power to fly. That fight was written in a way that wouldnt insult the audiences intelligence by keeping plausibility in mind when showing what we would expect to see when watching a farmer fight a soldier.
Has there been anything in on Supergirl recently that would cause us to expect Kara to have a greater strength or resistance to injury than Kal? Because I remember an episode where Reactron almost killed her in a junkyard, and Superman showed up to intervene. Reactron hit him with the same lightning attack that dropped Kara, and Kal just stood there tanking the attack; spooking Reactron into fleeing. Now in the season 2 finale, for no apparent reason Kara is able to slug it out with Kal and knock him unconscious. I don't care if they wrote in 'Kara drops, exhausted' afterward; it's still a BS outcome.
This fight in Supergirl was handled very poorly, and fans are right to be annoyed. The Supergirl fans are Superman fans too. Those watching the show had cause to believe that Superman should have been a much bigger threat, because on paper hes got every advantage. Kara managing to defeat Superman is one thing; straight-up overpowering him (given whats already been shown) is something else. The people complaining about the "Girl Power!" message lowering the quality of the show have a legitimate gripe, and the writers had better calm that down, or they are going to screw up the opportunity they have by alienating more of the people who would otherwise want to see it do well.