I've done both tours a few times over the years. Greatly prefer the Rotunda/Throne room. Much more interesting formations to see.
We usually stay at Tombstone Territories RV park not far. Huge spots and quiet!
The no cameras, phones etc. isn't so much about not taking photos but rather the fact that so many people drop things all over the caverns. It is a living cave and after having so much to clean up they've said you can't bring much of anything in. That said they do not inspect anyone. If you have your phone in your pocket you'll be allowed in just fine. If you take it out inside they'll ask you to put it away.