Sardinia vs. Sicily

I have not been to Sardinia, so I'll limit my thoughts to Sicily. While I suppose you can take a long train trip to Sicily, why not take a short flight from Naples (into Catania or Palermo)? It will be quick and inexpensive, and a lot less tiring. The bus system and train in fine in Sicily but in some areas, only regional trains predominate (they are rather slow). You cannot count on either trains of buses on Sundays or holidays (unless you have a very flexible schedule and can work around public transport). If you have 10 days in Sicily, you will need at least 2 bases..it really depends what geographic reach you're looking for. One base will (likely) not suffice unless you want to stick to one region and make very short day trips from that base (for example, a base in Siracusa is convenient to a lot of other sites in southeast/hyblean mountain region)...still, you will get tired of going back and forth from only one base over 10 days. Probably 2 bases is good, and 3 bases means you're going to have a very aggressive travel schedule. You can easily get by with public transport, but having a car will probably be more efficient. I'm sure there are no cities in Sardenia that are in any way comparable to Palermo or Catania (in terms of population density, "feel", and attractions), so that's one key difference (probably a lot less archeological treasures out on the countryside as well).

Here's an old thread from this forum on Sardinia. Hopefully it will help a bit.
https://community.ricksteves.com/travel-forum/italy/sardinia-a4b6bf34-12f0-4f41-aa46-cc7c08ab1f7f

Have done three trips to Sicily and one to Sardinia, all using rental cars. They are different in culture, history, and infastructure, BUT(the "great verbal eraser") to give you a taste, Sardinia is where Italians vacation and where Sicily is where tourists vacation.
To start with Sardinia, we flew into Cagliari, and drove the west and North coast coast and then back to Cagliari through the center. Sardinia is "off the grid Italy," other than Algerho where many of the budgets fly to. We stayed in Cagligari, Orestano, Algerho(our #1 city) and Saint Theresa. We drove the West and North coasts and every turn was a Kodak moment. It's not a dense historically as Sicily, as far as sites and churches and much slower paced. Finally for Sardinia, the wines there are world class and vineyards welcome guests outside of siesta(noon to 2 or 3).
Ah, Sicily! First of all I say rent a car to tour outside of Palermo, and decide to do either the West or East; we are partial to the West, with 2-3 days in Palermo along with visiting Monreal, and have based in Erice for its spectacular views and ease of access to Segesta, Sellunite(?) and Agrgento. We where there one year on St. Josephs' feast and visited Salami which really puts a show on along with unbelivable dough scupltures and exhibits. You can train or bus to Cefalu from Palermo, and well worth the trip and a couple of days and the hike to the top of the butte above the city.
Doing the East(and South), we base in Giridano Naxos, a quiet beach town below Taromina, and do day trips to Syracuse, Etna, and the Villa Amenia.
Finally, we will return to either the West of Sicily or back to Sardinia either fall of '17 or Spring of '18.

I think you mean "Adriatic Coast".

From Matera, you can take the FrecciaLink bus to Salerno and then take the train to Sicilia, if you prefer not to fly. Overnighting in Salerno would not be bad, and it would break up a long train trip. The FrecciaLink bus departs Matera in the afternoon.

You can visit Sicilia by public transportation, I always do it that way when traveling solo, but you have to plan well. You could do a nice concentration of either the east or west, or you could cover the whole island in ten nights but it would mean a lot of time spent juggling bus and train schedules. Buses are reliable but Sunday/holiday schedules are curtailed or nonexistent. I usually take three weeks for Sicilia, but I travel slower than most people.

Haven't been to Sardinia.

Seeing Sicily from two bases means a good bit of time going back and forth, and travel time tends to be longer by bus or train than in a car. I managed without a car and saw a lot, but I had 18 days and skipped Agrigento, Segesta and Selinunte. You'll need to spend some time with a guidebook and make a list of your top-priority sights, then check travel times from your potential base cities to figure out the best options. Rome2Rio will identify the segments for which the train is an option. Where there's no train service, you can follow Rome2Rio's links to the appropriate bus companies for schedule information. If at all possible, scrounge an extra day or two for Sicily and establish 3 or 4 bases. It's a fabulous island, and you will be very glad to have the extra time there.

Since you mentioned churches: Palermo has a wealth and great variety of churches and oratorios. Visiting days and hours vary, so you can pretty easily make full use of your time in Palermo, no matter what days you are there. Seeing working churches on Saturday can be a bit of a challenge, however, because they are often occupied with weddings. You'll also enjoy the local markets, and Palermo is a good base for a side-trip to Cefalu (along the coast to the east). Monreale (a must) is so close that I'd hardly call it a day-trip. With a car, day-trips to Selinunte (south) and Trapani/Erice (west) would be possible. Agrigento (over two hours) would be pushing it, even with a car.

I'd make my second base in Siracusa, whose historic Ortygia district was my favorite stop in Sicily. It's a good base for day-trips to Ragusa, Noto, Modica and Scicli. Taormina's about 2 hours by train but less than 90 minutes by car. Also possible by car would be the interior city of Piazza Armerina with the nearby Villa Romana del Casale (great mosaics).

Getting to Sicily by train will be a slog. A bus might be a bit faster if you depart from Matera but still would mean a full day on the road. I like the idea of flying. There are no direct flights from Bari, so it might work best to see the Adriatic destinations and Matera first, then the Amalfi area, then fly from Naples as previously suggested. If you prefer Amalfi first, then the Adriatic and Matera, your flight options from Bari will require a change in Rome and will take over three hours. You can fly into Palermo or Catania.

If, as you work on your itinerary more, you find the time available for Sicily/Sardinia shrinking, I'd tend to head to Sardinia, which I am sure is really lovely but which I think doesn't require quite as much time for a reasonably comprehensive visit.

Here's my VERY detailed trip report about my visit to Sicily in spring 2014. You'll see that we had 11 days, with a car, and ran around quite a lot, and still hit only the barest of highlights: https://community.ricksteves.com/travel-forum/trip-reports/sicily-palermo-caltanisetta-siracusa-taormina

I agree that trying to see "Sicily" from one or two places means a LOT of driving, although you can of course see just sections from each base.

I also agree that flying to Sicily is much faster and easier than taking the train. If you start your trip on the southern mainland and work up to Sorrento, you can take the Curreri bus direct from Sorrento to Naples airport, then fly to either Catania or Palermo. Catania is actually a bigger airport with more flight options. To see varied parts of Sicily, flying into Palermo and out of Catania, or vice versa, works well.

I've never been to Sardinia so I can't compare, but Sicily is great! Except when I was at designated tourist attractions (like the Villa Romana del Casale or the Greek temples of Agrigento), or in Taormina, locals definitely outnumbered tourists - heavily. And while Taormina is "touristy", it's also wonderful. As you'll see in my trip report, my friend loved the markets in Palermo and Siracusa, and I agree that the churches in Palermo are wonderful. So, Sicily certainly ticks all your wish list.

Caveats: I've been to Sicily (once), haven't been to Sardinia yet, but am currently planning a trip there next year (fall).

IMHO both of these places are best done with a car. Sicily does have some trains and a bus system, but relying on those will really eat into your time. Got unlimited time? Great, enjoy the slow pace of public transit. Limited time? Fuggedaboudit - just rent the car.

From everything I've seen, there are very, very few trains on Sardinia and the few that exist are not optimized for tourism - at all. I think for Sardinia, a car is pretty much mandatory, unless you're just going to fly in and go to a resort and stay in one place (which would be a shame, as the place looks amazing).

If all you have is 10 days, it seems like a no-brainer to me: fly to Sicily (that buys you a day) and rent a car (that frees you to see more).

Hope that helps.

I have commented about Sardinia enough in the thread linked by Agnes. Go there and you will get enough info on it. My "colleagues" above furnished enough info on Sicily.
I will give you my opinion. I love Sardinia, but its number one feature is the amazing beaches and seawater. If you were going in summer, I'd go there in a minute, no questions asked, but in mid October? If the weather holds, ok, but it if it turns rainy, then you won't enjoy it as much.

JerryG:
You get an F in spelling.
Don't they teach you how to spell geographic names in school in your Wurstel Salam, North Cazzolina?

Sorry! Meant Adriatic Coast.

Thank you all so much for taking the time to comment. It has been most helpful!! I think it will be a flight into Sicily, with a car for at least part of the time. And maybe starting the trip earlier in September - I was just trying to get past the high/hot season, but would rather not get into rainy season either. I had in my mind to start on the Adriatic Coast and move clockwise, but perhaps starting in Naples/Sorrento, moving counterclockwise to Sicily and then Adriatic Coast would be better with weather/crowds? In the scheme of things, it probably wouldn't make much difference weather-wise. Hard to forecast the weather!