Naples to Sorrento

If you are arriving in Naples after a long journey (like from overseas, or with children or elderly, with tons of luggage, with some other need), then sure, why not splash out--that is what money is for, and it is not a large amount in the trip budget. OTOH, if you are just arriving at Naples train station or departing from the city, then I see no reason to not just take the commuter train. Weigh your own situation and comfort level with public transport.

Only you can decide what's "worth it."

The train is scruffy - then again, so is Naples (so watch your belongings like a hawk on the train and in/near the train station, but you should be doing that everywhere, no?). The train takes you where you want to go. The train is reliable. The train is no-frills. The train is cheap.

Hiring a private driver is expensive, but less scruffy.

I took the train, like most people do, and it was perfectly OK for me.

The nonstop bus from the Naples airport to the train station in Sorrento is so easy and only 10euro. Two minute walk from the airport terminal to bus depot. Driver or taxi will cost you at least 100euro.

Month and year? Hotel or AirBnb? Length of stay? Party size? Location in Sorrento? Age and mobility? Travel experience level?

If you are staying at a bargain hotel in Sorrento, you probably need a taxi from the Circumvesuviana station. That could be 15 Euros or more. That makes it easier to pay 110 (?) Euros for a car service from Naples, doesn't it?

Your question is reasonable, but it's not possible to give a certain answer. If you use your hotel's land-partner to provide the car service, it's easier. But if your plane is late and you miss the train you expected to Naples, then it's not effortless anymore. Lots of travelers here are VERY price sensitive, however. We found it easy to spring for a car service return, after jamming onto the Circumvesuviana with our luggage for Sorrento arrival in the last week of May.

The "scruffy" train alluded to above, the Circumvesuviana, was fine for me when I used it to travel to Pompeii an Herculaneum (on different days), but that was in February-March. The Circumvesuviana isn't air conditioned. I doubt I would have considered it "fine" in the summer.

Depending on time of year you also have the option of taking the Campania Express

https://www.positano.com/en/campania-express-train-schedule