I have both pins. Pirates has an awesome toy- a freaking pirate ship that breaks apart and sinks down into the playfield! That's pretty awesome. But setting that aside, lotr dominates on the rest of the topics, and is much more of a keeper. The ship shot on pirates seems to be easier to hit than any shot on lotr for new players, but once the ship is mastered and the ship sink thrill wears off, you will wish you had bought lotr. Especially if you love the movies. Although guests are drawn to pirates over most others.
Value- I bought both for the same price which i considered both at market value and they both seem to have started to shoot up 2-4k in the last year.
Shots- Lotr is considered by many to be a "top 10 all time shooter" and the legolas ramp shot still gives me happiness after the 1000th shot. So smooth. And hitting the center ring shot never gets old either. None of the pirates shots are memorable IMO.
Theme- lotr is movie themed. Pirates is just, well, 'pirate' themed.
I like pirates but honestly it is my current least favorite game that I own (something has to be last) and I have almost traded it off twice now on deals that fell through. Lotr is bolted to the floor.