The identity-memes are the only reason the question even exists. Historical pirates were mostly desperate or ambitious but otherwise ordinary sailors, and usually had pretty short careers. Historical ninja were usually dirt-poor burakumin without much in the way of reliable support, and -- in common with a lot of other historical assassins -- were individually used more as ammunition than as soldiers. I'm having a hard time coming up with a reasonable scenario in which they (as opposed to the pop-cultural image of either one) would have any incentive to fight, and if you stretch to create one the outcome would be almost completely determined by the circumstances.