Positano vs Sorrento

Positano is smaller, on the beach and spreading up into the hills. Positano is better if you intend to stay and enjoy beach. Sorrento is better as a base for day trips. Good bus, train and boat connection to almost everywhere around.

peg,

Positano is not as convenient for transportation as only bus, car or boat access is possible. If you were planning to just stay there for the entire trip with perhaps a day trip by boat to Capri, that will work. However if you were planning for wider variety of day trips (Pompeii, Ercolano, Vesuvius, Naples, Capri), then Sorrento would be a better choice.

The center of Positano by the beach is awesome, lots of restaurants, shops and the scenery is the best in all of the amalfi coast. I have been there twice and love it. Dan Cortigiano

I prefer Positano. I find it quainter and more quintessential of an Italian fishing village. Also better beaches on that side, not much in Sorrento.
However without a car it is not as convenient for some day trips (like Pompeii, Ischia, or Naples). It is however more convenient to visit the Amalfi coast (Amalfi, Ravello, etc.) and is just as convenient as Sorrento to visit Capri by boat.
Positano is perched on a very steep cliff with uphill streets and steps, therefore some elderly travelers, especially with mobility problems find Positano not ideal and too strenuous. But you seem to be a young family.

Thank you very much for your help! Great information :)