Tubs are usually preferred because they generally hold humidity much better than tanks, and are easier to clean. Plus, they're MUCH cheaper, haha.
Both Sterilite and Rubbermaid are used, yes. Holes can be bored or melted around the tubs to allow airflow. The biggest downsides are they're not that pretty without some work, and don't hold heat like glass can. (Not too much difference, though.)