They both have really great main toys, but they both also get very monotonous if you have a long game.
Random pros/cons
-POTC wins for sound. I really like some of the music (especially Collect Crew), and I think the voices are very well done, even though others have different opinions. Batman's voices are truly terrible.
-BDK gets points for a moving interactive toy. The way it works on the later levels w/ the inserts is really challenging (you have to hit the crane as its position is matched w/ a moving insert). POTC's toy, while stationary, is very cool due to multiple levels of damage (sails drop) & animation FX. It rocks back and forth and sinks - revealing the Kraken shot.
-BDK is a bit more flowy, if that's important to you. I'm no "flow snob", but sometimes it does get annoying that EVERY shot in POTC stops the ball. Nothing flows back to the flippers really.
-I really like the Tortuga multiball. It's a clever use of the spinner...the # of balls you get in multiball depends on how many you trap in the spinner before the time runs out.
Neither game lasted more than a few months in my collection...but POTC is certainly unique...I have to respect it for having such a different layout than most modern games. Of the two, if I was going to bring one back into my home, that one might be it.