I know, I know, it's an old debate that's been beaten to death, but I thought I'd throw my two cents in.
First of all, I think it'd be best to say what side I'm on to get it out of the way: I prefer pirates.
I've never been crazy about ninjas simply because they have no personalities. Think about it: Your typical ninja doesn't even reveal his entire face, denying us a huge chunk of potential expressions. They're always jumping around, looking real cool, but what else is there? Any good writer ought to know that mere skills, no matter how impressive, do not make for a compelling character. Ninjas are almost always identical, faceless assassins that merely serve to get in the hero's way. I've never even heard of a ninja who had a distinctive personality, appearance, or much less played the main character.
If you ask me, there isn't any comparison. Pirates are extremely flexible characters, with an array of costumes, voices, weapons, quirks, ethnicities, and potential positions on the scale from good to bad to choose from. They can even be supernatural. I've heard the argument that pirates are dirty, scruffy characters (which is actually part of the reason I like them), with no style or grace, while ninjas have grace to spare. Who says a pirate can't be graceful? What about Douglas Fairbanks and Errol Flynn?
I honestly think it's better to make a comparison of pirates and cowboys. But the trouble is that they both has similar advantages and a similar flexibility, while the main difference is that one is skilled on land, the other at sea.
It is perhaps best to ask ourselves what the differences between pirates and kung fu warriors are. Kung fu warriors can have any kind of personality they please, as proven by Kung Fu Panda. Or perhaps samurai. But it kinda boils down to aesthetics, really- what environment the stories take place in, what fighting skills they possess, and the style of the costumes and art.
When you get down to it, it's all about aesthetics. You could compare pirates to old-school gangsters, or medieval knights, or barbarians. It's all kinda depends on what they wear, what weapons they use, what time period it takes place in, and what the buildings look like. Everything else is fair game.
But so long as ninjas remain one type of ninja, I don't think the rivalry is valid.