I've been to both and both were nice. If I were to go again, I think it would depend on what I wanted to do, for a big city break, I'd pick Italy, because I've been to Athens, but I've never been to Rome, Florence, Naples etc. For driving around, visiting small villages etc. I'd go for Italy. For a beach vacation, combined with a couple of short excursions, Greece.
Both are very rich in history, museums and culture. And the food is great. Ah, Italian ice cream and Greek souvlaki.