I have both. Monster is plain fun lots of shots but relatively easy to pick up and play. Monster Bash is pretty easy to get to just need to start all the modes. I really like mosh pit multiball. Monsters of Rock takes a bit more as all modes need to be completed.
Lord of the Rings is super deep. I got mine new in 03 and have not even tickled Valinor. I have completed all the modes just never in the same game. I have destroyed the ring many times and have done there and back again several times. It is one of the best two flipper games ever made. All modes are just exceptionally done, stacking gollum multiball with say return of the king multiball gets great scores.
When family and friends come over the more casual players like monster bash, It is just a fun game to pick up and play with a great theme, but the guys that play pinball enjoy Monster Bash end up at lord of the Rings.
Neither will leave but if I had to pick one Lord of the Rings would be it. It also helps that it goes for about half of what a decent Monster Bash sells for. Good luck!