Sorrento/Amalfi Coast

My opinion:

I find Amalfi Coast/Positano more quaint, more romantic, prettier villages (check for yourself using Google Images).
Sorrento: bigger town, more convenient for transportation to Pompeii, Ercolano, Naples, thanks to the Circumvesuviana train.

There are boats to Capri from Positano, Amalfi, and of course Sorrento.
Boats for the Amalfi coast stop at Salerno, Amalfi, Positano.

If you stay in Positano and want to visit Pompei, take the Sita bus to Sorrento or to Meta, then proceed by Circumvesuviana train from either station.

We love Sorrento best...and find it beautiful, quaint, charming, relaxing and very fun. And, as Roberto said, the most convenient town to get to other places.

There really is no wrong answer.
I prefer Positano if given the choice. Have stayed in both and if we return the area we would book in Positano again but not Sorrento again.
That said, Sorrento is the better choice logistically both for coming and going, visiting Pompeii if planned and also visiting Capri (both have ferries running but the Sorrento ferry is less likely to stop running in case of rough seas) and I really would not mind staying in either town. I would say on average it is less expensive as Positano is a pricey town.
Your budget would probably net you a nicer place in Sorrento.
Larger town so more options but loses the uniqueness Positano has due to it's smaller size.
Both have nice views but the view is different and I prefer the views in Positano which are seen from everywhere.

Thank you everyone. I am still torn between where to book. I will be traveling from Rome and just want a place with a great view and access to different places. I am in the process of looking now.

Sorrento is the place you want to stay. Better access, very lively even at night. If you choose right hotels - great views. Positano and Amalfi are quite smaller, no train connection (unlike Sorrento), less frequent bus and boat connections (than Sorrento).

I prefer Positano. But as you can see, to each his own.

De gustibus non disputandum est.

Sorrento is more accessible and a little less expensive. I have stayed in Positano and Sorrento and I prefer Sorrento. Positano is very expensive and in the evening there is little to do. Although after a full day of touring you may want to just stay in and relax after dinner. Sorrento is more lively and just as lovely as the other Amalfi coast towns. But really, you are in Italy, have a great vacation.

Lorieann

I had the same conundrum on our visit last May.

We stayed in Positano at Albergo California with a beautiful balcony over the town:
We were steps from the bus stop where we took the bus up to Nocelle to hike the Path of the Gods.
We rode the bus to Amalfi and up to Ravello. And then rode the ferry back into Positano.

Then we took the bus to Sorrento to stay at Hotel Minerva - the most amazing balcony !
We walked into town every day and wandered.
We took the ferry to Capri and did 5 hikes around the island.

We loved each location immensely but we found each spot allowed us to do different things.