My wife and I took the boat tour out of Sorrento to the Isle of Capri two weeks ago. I just wanted to give it a thumbs up and recommendation, and maybe a piece of advice. The crew, the boat, and the itinerary were all great. We met very early at the Marina Grande in Sorrento and after a few formalities, we headed out. Unfortunately, the seas were up that day, and it is not a big ferry-style boat, but it is a sound craft in great condition and I felt very safe as the captain took the rolling seas at a good angle and speed. The ride across the bay was comfortable and scenic. There were 10 or so passengers and a crew of three and they were helpful loading everyone into the boat.
One passenger with limited mobility had a little difficulty boarding but the crew handled it extremely well. You may want to consider that boarding/unboarding in high seas could be difficult for some. There is no gangway or ramp, you step from the pier right onto the boat, and the deck may be rising and falling with each wave. It's a matter of timing out the roll, and it helps to be a bit nimble. There are two crew members standing by to help each passenger.
Sadly, the Blue Grotto was closed that day due to the high seas, always a possibility there, but we made the best of it. We were delivered to the main harbor and given several hours to explore the island. We rode the funicular up and then took the bus up to Anacapri, which was beautiful.
After meeting back at the marina and reboarding, they handed out sandwiches and we took a circle around the island, stopping at some very pretty caves and coves, gaping at the amazing sights and taking 1000 photos. The ride home was easy and we all had a farewell shot of limoncello pulling into the harbor. Very enjoyable day!