Both of my older two boys went straight into Calc III after earning 5's on the AP Calc BC test. Both, despite being VERY strong in math, struggled. It seems there was stuff they were expected to know that they somehow hadn't mastered, despite the high grades and AP scores.
Son #3 just got his junior year AP scores back. 5 on AP Calc AB. He'll take BC next year. Were sons' 1 & 2 experiences an anomaly? We're thinking about insisting that son 3 take no higher than Calc II as a freshman, no matter what he scores on the AP exam.
What are your kids experiences with college calculus after AP calc?