I got an in-line centrifuge ("squirrel cage") from Broan or Nutone a few years ago. 200CFM capacity. We like it. It is quiet and powerful. In the other bathroom we bought a fan that had motor blades, and it makes an irritating noise. It was 120 CFM. FWIW, I'd put my money on a squirrel cage any day.
No matter what, steam still fogs mirrors when the shower has run, but you can see the level of the fog line rising every minute as the fan keeps pulling air out.
The more powerful the ventilation, the more you have to plan for make-up air to come from somewhere else.