Moaning Caverns has one overwhelming distinction: it has the largest underground opening in California. The 180 foot tall main room could actually fit the Statue of Liberty (but good luck getting it through the narrow cave opening)! There are other interesting features, but size is everything here. I've been to Carlsbad Cavern, and it is in a class by itself, but I've also been in many caves in California, and none has a room to match this one.
One can also rappel. Um, no thanks, I'll take a rain check.
The owners of the caves are quite decent about providing discounts for student groups. They can be contacted at http://www.caverntours.com/MoCavRt.htm.
PS: "Moaning"? I didn't talk about the name, did I? They say today that it is from the particular way that dripping water echoes off some of the rocks, but I remember hearing (this isn't hearsay at all!) that the pressure differences caused a very strong airflow through the original entrance that would whistle and moan like a ghost. The development of the cave nearly a century ago destroyed the effect.