I'm applying to mostly academic places, but I did interview at 1 private practice and spoke to people from 2 other private practices.
There is huge variation in practice structure, even within MEDNAX. The 2 former fellows who work for MEDNAX now really love their jobs, and they are completely different. I've seen anything from only 24 hour shifts, to 2 weeks on service at a time with intermittent home call, to 1-2 week service blocks with dedicated in-house night call people and 24 hour shifts on weekends. I imagine there are several other structures out there.
The general takeaway is that in private practice you will have more clinical weeks on service, but when you're off you will have limited/no responsibilities (research, teaching, etc.).