I don't think either public or private is better, but it's good to have choices and options as a parent. In our case the application process was somewhat arduous, but in retrospect this weeded out a lot of folks (parents and kids) who were not 100% committed to the school and to making things work. It's not a casual thing.

The scale of private schools is also nice - everyone can know me, my spouse and my kid. This gets harder as schools get bigger and bigger.