Airports in Sicily - preference for arrival/departure?

When we planned our trip to Sicily, we chose the order of the airports to fly on and out of by the flights offered to our next destination which was London Heathrow to connect to our international flight home. We ended up traveling around Sicily in reverse order of what we had thought we would do due to our needed flights.
Your next destination is Naples( a good one!) so look for the best prices and times for flights there from both airports. There are also options of ferries from Sicily to Naples.

Sounds like Palermo is similar to Naples. Perhaps you should start in Palermo to break up the larger cities. But then, if Sicily will be at the beginning of your trip from the US, maybe start in Catania. Sounds like the area around Catania is more relaxed. We're going to Sicily in March. We're planning to fly into Catania and out of Palermo. We'll be renting a car between the two cities, seeing many sights along the way.

There are no advantages of one over the other. Only as it relates to the logistics of your itinerary. Time, mode of transportation - car rental or public transportation are other factors. What are your sightseeing priorities.
If you plan to spend most of your time on one side of the island, say, the eastern side, then flying in and out of Catania makes the most sense. Same if you're concentrating on the western side - use Palermo.

Thanks for the comments. It makes sense to me that the primary consideration is the timing and convenience of connections. Wherever we fly into, we will likely explore that area via public transportation, then pick up a rental car to travel to a few areas on the island. So hard to whittle it down, but I know that fewer places for a longer stay is best! We won't actually be staying in Napoli, but will fly there after Sicily and get public transportation to Sorrento (or similar) to explore Pompeii, Capri, and possibly the AC. From there to Roma for a few days and the international flight home.
So excited!

Although Catania has a slightly bigger airport in terms of passenger traffic, however you can find non stop connections to NAP from both PMO and CTA.
From PMO you can fly to NAP with Alitalia or Volotea
From CTA you can fly to NAP with Alitalia or Easyjet or Meridiana.
Check all the above options and see which works best for you.