a ninja pirate would be a pirate that acts like a ninja, meaning he'd be sailing the seven seas but be kinda dark and sneaky all the time
the pirate ninja on the other hand would be a ninja that acts like a pirate, which is much better because then he could be one of those ninja's that have their own... "thing", and his would be yelling "ARRRRRR!" right before every decapitation
Pirate Ninjas, bucause the way you worded that makes it so that this choice is a ninja, who, at some points in time, goes around as a pirate... While, ninja Pirate, is a pirate, who sometimes goes around as a ninja... and can you really imagine Captain Jack Sparrow trying to be sneaky? he's not very good at that... While a pirate ninja (AKA, Captain Sam Fisher) Could blow up your ship after he sneaks on board and quietly kills everyone... Oh yea.
Ninja Pirate= A particularly skilled Pirate that is sneakier than the average pirate- Instead of blowing you to bits with its gun it would rather stab you in the heart while you are sleeping. A Pirate Ninja, however, = A ninja that has gone AWOL from it's pertained allies. It steals, will destroy things that aren't not necessary to destroy, and will take up the practice of swordsmanship and gun-handling...
Hmm.... looking at my two definitions of the two, I'd initially go with a Pirate Ninja, but I think that a Ninja Pirate would be cool...
A ninja pirate would be a pirate with the skills of a ninja. A pirate ninja would be a ninja with the hygene of a pirate.
I think the choice is obvious. Ninja pirates are pirates first (contrary to visual logic), and since everyone knows that pirates are awesome, ninja pirates must ALSO be awesome. Piratical assassins. Delicious.
Ninja pirateirate who acts like a ninja Pirate ninja=ninja who acts like a pirate Silly ninja, you have lost most of your stealth. Your skills have degraded. Pirate, good job. Now you can plunder and steal without anyone even noticing!
Ninja pirate. Clearly, you start off growing as a ninja, until your clas was destroyed and killed the clan that destroyed yours. Having nothing left to live for, you went to see, only to be picked up by a Captain who understands your skills.