It depends. If Snake Eyes wanted to defeat Storm Shadow, he
could.
But he always seems concerned about Storm Shadow's feelings and ego. So he
would let Storm Shadow win to save his honor.
If Snake Eyes is distracted by feelings, Storm Shadow might actually defeat him.
My 6 year old says Snake Eyes would win by hiding up on a building, then jumping down and defeating Storm Shadow, falling on top of him to break his back.
Snake Eyes is the best, but he doesn't care about contests, so he will let Storm Shadow win, because Storm Shadow DOES care about contests.
