Last year, I've completed the CCQ (Cross Crew Qualification) between the A320 and A330. All the systems between the A320 and A330 are almost the same. The A330 has some things more (due to for ex. ETOPS) but in general there are not many differences.
We did only 4 simulator sessions for a complete type-rating just because of the common systems between the Airbus FBW aircraft. The procedures in case of normal and abnormal situations are just the same between the A320 and A330.
Even flying is the same. A month after starting to fly the A330, I had still the impression to fly the A320.
This is the way it should be !!! It can save a company a lot of money.