We are planning a 2 week trip to southern Italy this fall.

Any advice on whether we should spend our time on the Amalfi Coast in Sorrento or Positano?
Which is a better base for exploring the area? How may days should we plan to stay?

Base in Sorrento. Easier to get ferries to Capri, connections to Naples, Pompeii. Then perhaps plan a few nights further along the AC, depending on how far east you wish to go -- Ravello? Meanwhile check out ferry schedules, private drivers. Or will you have your own car? Hotel or apartment? Don't count on the public SITA bus, it's on its own whim as to schedules.

Positano is nicer, IMHO, but Sorrento has better transportation options.

It depends on where you want to go when you're there.

If you like the sea don't forget do drive a little south around the Cilento coast, amazing water there.

When in the fall are you coming? Sept is one thing but Nov is a whole different issue (many places will be closed for the season and ferries have pretty much stopped except to Capri and Sorrento).

It totally depends on what you want to see while you are there. If you are more interested in seeing Pompeii, Naples, Vesuvius, Herculaneum and Capri, then staying in Sorrento makes sense.

If you are more interested in seeing the Amalfi Coast (Positano, Amalfi, Ravello, Vietri, etc.) and Capri, then it makes more sense to stay somewhere on the Amalfi Coast (Sorrento is near but not on the AC).

We spent 6 nights in Sorrento using it as a base for the entire area and absolutely loved it. We spent time in Sorrento itself (usually around dinner time and strolling around in the evening) and took day trips as well. Was easy to get to Pompeii/Vesuvius, Naples and Amalfi coast towns. One day we hired a driver who took us all around the Amalfi coast towns. Can also do it on the bus from Sorrento. And another day we went back to Positano on our own on the ferry from Sorrento. You can also get to Capri easily from there, either as a day trip or spending more time there. We actually spent 3 nights in Capri after our 6 in Sorrento. I went back and forth before the trip about where to make our base, but I could not be happier that we ended up choosing Sorrento.

If you want to explore, choose Sorrento. It is a dull, nondescript dormitory town but perfectly situated for rail and ferry transport as indicated above.