Cannot you visit both ?
Anyway, if the focus is the great food, in my opinion, the score of Sicily is a bit greater than the score of Sardinia but, I want to be very clear, both islands could deserve.
In Sicily, in Catania I suggest you two nice restaurants not yet famous to the tourists but very well known to the local people:
Not far from the main street Corso Sicilia, the restaurant is AL GABBIANO (www.ristorantealgabbiano.com) ;
then, to dine and drink wine: RISTORANTE METRO' (www.ristorantemetro.it).
At the feet of Etna, in Santa Venerina, a very delicious and comfortable D&B: SAN MICHELE, located in the winery Cantine Murgo, so that wines are excellent (www.murgo.it).
If you go to visit Piazza Armerina, do not miss the restaurant AL FOGHER (www.alfogher.net). It is a gorgeous restaurant !
Between Messina and Palermo, but closer to Messina, not far from the wonderful beachs but already close to the mountains, there is the small town of Capri Leone; well, there is a cute and confortable D&B: ANTICA FILANDA (www.anticafilanda.it).
A good place to sleep in Messina is the B&B LE CASE PINTE (www.lecasepinte.com).
Anyway, in May I wrote my notes about my last trip in Sicily (I spent there the whole month of March) and I can send you, if you want, further informations about smart places.
I have not been to Sardegna, but I have been to Sicilia, and I think about the food and wine experience we had there on an almost daily basis. To me, it exists as the Platonic ideal of Mediterranean food.
Although not as good as Palermo for food, I disagree that Taormina is not a good food destination. Branzino alle Messinese at Maffei's or pasta with Etna mushrooms at Osteria Nero D'Avola are as good as food gets.
I've only been to Sicily, and again, the food was amazing. The wine too, all influenced by Mount Etna's rich soil. We loved DonnaFugata's wines, as well as Planeta.
One meal we will never forget was in Erice, which is a very romantic hill town of castles that are still occupied. They use alot of peanuts in their pasta sauces, delectable!
Sicily was occupied more, thus more culinary influences. I'm sure Sardinia has some phenomenal food, but I would opt for Sicily. Just stay away from Taormina for food. Marsala, Palermo, Siracusa, Trapani, Cefalu, Ragusa, Agrigento, Catania are all fine food destinations, as are the hilltowns and small coastal villages. I've been 4 times and the food haunts me everyday.
I stayed at the Romazzino (Costa Smerelda, Sardinia) several years ago and the food there was indeed stellar (of the very high end stellar variety), plus on the full board arrangement we had you could eat at several other related hotels (Cala di Volpe was one of them) which were also stellar. However, we found no chowish opportunities on our explorations of the countryside. So it depends whether you want stellar high end delivered to you without effort or whether you enjoy seeking out chowish spots, for which I think Sicily might be better suited (without, however, having been there). Mind, my stay at the Romazzino was quite awhile ago. For my own taste, much as I loved every morsel of food I put in my mouth while there, the ultra luxury full board arrangement is not my idea of a chowish holiday (I wasn't in charge of that one).