Realizing there are many private/public boat/ferry tours/trips: what's the difference in cost & experience comparing one example tour/trip?
That's pretty much an impossible question being there are 'many' options.
The 'public' boats are the ferries. These are not tours; they just get you from point to point. Schedules and prices are on the websites, although they've not been posted for spring/summer yet.
https://www.naplesbayferry.com/en/t/sorrento/amalfi
Tours will generally be on private boats, and group sizes/prices will vary.
It can also depend on where you're departing from, and season (ferries don't service most of the coast in the winter)
What is it that you want to do?
There's also the issue of time of year. Crowding, assignment of larger (300 passengers and more) boats, more frequent service, lower seas leading to fewer cancellations. On one peak season Capri-Sorrento ferry we took, it was standing room only, kind of like a subway car at rush hour. I hope the boat wasn't "overloaded". (It had cars and trucks too, so it was a high-capacity boat.)
It matters which ports you use; Positano in particular has some limits on boat size. That may sound good to you, but it increases competition for scarce seats. I get seasick easily, so I wouldn't care to go from the mainland to Capri in a small, open boat. Many people mistakenly believe that their ferry is going to have dozens of open-air benches on top of the cabin. That's not likely.
There is also a wide range of budgets on the AC, ranging from very wealthy to backpack-budget. Someone recently posted about a one-way car trip from Sorrento (or was it Amalfi) to Salerno. The point is, a one-way trip is going to require paying for a "deadhead" (nothing to do with rock and roll) trip back home for the conveyance. And if a boat or a car is going to wait for you (say, on a private trip to Capri), you're going to pay for that service.
Just do a search here on the Forum; recently there have been 2-3 posts a day on the Amalfi/ Sorrento area and related activities. You could also just read all the posts under Italy for the past 6 months- there's a wealth of info, and your questions have most likely already been answered.
Safe travels!
Sounds like I have some research to do! Thanks for all the replies/suggestions.