The weather in both locations at that time of year is similar with Sicily being slightly warmer. My choice, if you have a minimum of 10 days, would be Sicily. Fly into Catania and leave from Palermo. I would spend the first two nights in Catania. (Fish market, WWII Museum, visit to Mt. Etna). Taormina is actually a small resort town that in April might be Dead but worthy of a day trip from Catania. I’m assuming you meant Siracusa and if so, definitely stay on the island of Ortigia. (Hotel Domus Mariae overlooks the sea and has a nice roof-top terrace.👍👍👍.) Great day tripping to Noto, Modica, Scicli and Ragusa. The latter also nice for an overnight stop.
Piazza Armerina is the town near Villa Romana del Casale where the remarkable mosaics might awe you. Onward to Agrigento and the Greek temples. (Baglio della Luna great rural hotel with nighttime views of the temples.) Then to Trapani on the west coast from which you could make a day trip to the hilltop town of Erice. (Residence La Gancia is a moderately priced waterfront hotel in Trapani.)
Now you drive to Palermo with visits to the Greek sites in Segesta and the magnificent Cathedral in Monreale. Palermo is almost a giant ZTL so make sure you get rid of your car before entering one.