After school care at school is easier in many ways, no extra work for you and no looking for a nanny. Kids just stay at school and usually there is some homework support, friends, and outside time. Win/win.
Nanny is better if your kids want to do activities and more flexible if you want them to be driven to do other things or if your kids have different needs (one of my kids likes to be busy, one needs more downtime at home).
Nannys are harder to find - especially part time after school - we have a full time nanny instead and we pay her to do other things during the day so we don't have the stress of looking every semester for a different high school student or whatever.