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I suspect this would come down to the setting. Obviously each character has their own home field advantage. Now, if you dropped them both off on an unfamiliar planet with no supplies and gave them a good reason to fight... I think I might give it to Picard. Assuming that they both try to McGuyver up a weapon, I somehow think Picard would be more effective based on the depth of his knowledge. I would definitely watch this episode, though.
