There are many things to think about.

How quiet do you want their rooms to be when the door is closed?

How do they treat doors---swing on them, slam them a lot, tape/nail/staple things on the doors?

Basically other than the above type questions, the difference is in fire code ratings. Hollow core doors do not have as long a burn time as most solid core doors. That means in a fire, hollow core are less protection.

I recommend solid.

handymax and palimpsest, thank you very much for your help. Mostly they'll swing on them, maybe once a month, my son might slam the door when he gets angry with his dad. They will never tape/nail/staple things on the doors. Will the solid core prone to warp due to the change in temperature or humidity? I am living in the bay area, and I hope this shouldn't be an issue.

With solid door, they may not need to put on earphone to listen to the violin or piano video clips. But I might not be able to hear if my son was properly playing violin.

If you're worried about warping, check out veneer doors. They are solid core, but he core is more stable and the door may even weigh more than solid slab wood. And the veneer should be thick enough to handle normal abuse. Also less expensive.

I grew up in a house with hollow core bedroom doors and they're all just fine 50 years later. Of course, slamming and hanging from them isn't something we would have contemplated.

Things aren't built like they used to be either. What's the price differential?

It all depends on what you want it to look like and what you want to pay.

Don't pay much attention to salesman. He most likely makes more on the solid core.

If slaming them is an issue then a hollow core is less mass to slam and less damage to jams and such.

Cheaper doors are cheaper to replace if temper tantrums are an issue. Save your money for better doors until abuse is out of the question.