First off I should say that my peds clerkship was a cluster...too much trying to be jammed into 8 weeks at the expense of inpatient experience. They somehow managed change the clerkship in the middle of this year, so I was in the last group to do it under the old system.
My one peds night was worse simply because I was on with an intern (an IMG, not that there's anything inherently wrong with them, but it compounded the issue) who had never been on call before - this was October mind you. We didn't get any pages after 9:30pm, but I still was up every 90 minutes calling into the ER just to make sure, because I didn't trust the intern to be okay on her own.
Medicine - I had great residents at the VA. They usually only wanted students to do 2 or 3 admits and they'd send us to bed. I only got paged once over the course of 4 overnights, to see a paracentesis done on a guy we were pretty sure had SBP. It was pretty perfect as we had just gone over SBP in our lecture series earlier that week.