I had a private OB but when I came down with a bad tummy bug at 34 wks I called the hospital. They had me come in and they called my OB when I got there.
I think if I'd called my OB he just would've said go into the hospital and I'll see you there so I don't think it makes much difference really.
ETA it was a Sunday night, if it had been during business hours I probably would have called his rooms.