Well, I think there are many factors we must consider in this debate.
One of the most poignant ones being the cool factor. Now, both the Pirate and the Ninja are cool in their own regard, but can one really be considered 'cooler' than the other? Let us examine their respective cool factor, if we shall:
General Appearance:
Ninja: The black sneaking suit, Katana, and ability to kill just about anything, with anything, is always a couple points of cool. The fact that you can turn around, and be staring death in the face adds a whole new level of coolness. Not to mention the fact that Ninja has effectively been tacked onto terms such as 'chop' and 'kick', and of course, 'Teenage', 'mutant', and 'turtle'.
Pirate: Pirates are swashbucklers, the ninja of the sea, if you will. What they lack in silence, they make up in hearty sea-chanties, boats, and buxem wenches. Like the ninja, the pirate also sports an amazingly cool outfit. The more flamboyent, the cooler, with extra cool points being awarded for either a monkey, or parrot on the shoulder, and a wide brimmed hat.
Background:
Ninja: Origins laying in the Orient, the ninja has a latent ability to fight, with all that Kung-fu hari-kari stuff. Not this whole Neo 'I know Kung-fu' crap, but the real stuff. The 'I-just-stuck-this-sword-up-your-ass-what-you-gonna-do-about-it' type of Kung-fu. I mean, this is the real stuff. These guys are assassin's, and the go-to guys of the government. While being tools of the government is a bit of a downside, they have proven time and again they're capable of screwing them over just as much as their target.
Pirate: Since the high seas became a venue of travel, so has pirates existed. Sailing on their boats, going from port to port, and giving sailors the reputation they have today. No, not the gay one, but the promiscous man-whore reputation. Not to mention the fact they are always connected with massive amounts of gold, women, and beer. Where's the downside of that?
Effectiveness:
Ninja: Ok, let's be honest here. ninja's loose points in coolness here. I mean, they suffer from a serious problem. Send one ninja to do a job, and no matter what it is, assassinate someone, steal something, halt and army of invaders, and damn, that job will be done hell or high water. Replace that one ninja with, say, a dozen, and damn, they somehow become useless! So, while looking cool, and acting cool, they are only cool when alone. Otherwise, they become fodder.
Pirate: Pirates recognize the fact they need to work together, but that doesn't mean they can't work alone either. A swashbuckling pirate has been known to fight their way of just about anything (
see Jack Sparrow). Not only that, but if you give them a team to back them up, all of sudden they become that much better. A pirate gets the job done, alone or with their A-team.
So, to sum up, I'll have to go with pirates. Women, money, booze, a monkey... How cool is that!