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I admit I don't know much about Barda, so I would be willing to change my vote if a Barda fan can give me good reason why she would win.
What I do know is she grew up on Apokulips and was trained at a young age to be a good fighter/killer. From what I have noticed is people have come paired her to Wonder Woman, but a slight less powerful.
She joined the British military, before stepping into the Captain Britain role (it ended badly). When she joined the X-men she was able to stand her own against people who were stronger then her in h2h. But when she used her telepathy she was a power house (in my opinion had a much better showing then Jean at that moment in time). Then when she stepped in to the seige perules she was brainwashed/ got a new body into joining the hand as their lead ninja. After much confusion we learn that much of her ninja skills come from the ninja Kwannon. We have no real knowledge of her back round so there is no way to know how great she really was. But Betsy using Kwannon's ninja skills showed some good fighting skills.
No knowledge of each other, Barda gets her rod and Betsy get her t/k blade (the one that looked like a you know what). Knock each other out
Knowledge of each other, Barda gets rod and her Aero-disk. Betsy gets t/k Katanna.
That's why I was not sure if Betsy having her telepathy helped in the battle. Like I said from what I understand Barda is another Wonder Woman (her being immune to telepathy reinforces this opinion). Getting harder to wonder why to even bother reading anything with her. Anyways to the topic :
@boob: Not likely. Barda's New God psysiology are just out Betsy's reach to do anything at all, even if Betsy's katana does proved to be strong enough to harm Barda (which is unlikely), She could easily outmaneuver Betsy with ease.
I just found out that its not the artistes not paying attention to each other when drawing her psi weapons (I always thought it was), turns out she can choose the size and width subconsciously. I should have chosen a size for each weapon, but then again it may make it more even. The other thing is she can treat her weapons like the Green Lanterns in the fact that they can throw what they conger, and then make a new one as powerful and/or stronger. And just as quick, maybe quicker. Not sure if that is fair considering Barda doesn't have much of a long range. If she does then Psylocke should be allowed to use her blade and katana that way.
@boob: I know about that. Anyways it might be possible for Betsy to brain shut Barda, but then again she will have to catch her to do so.