There are multiple factors to consider when choosing breed of honeybees to purchase. Let’s consider the climate patterns first and foremost:
Italian bees are known for the docility and high honey production. They also have greater survivability in mild climates (such as the Mediterranean weather common in Italy). A general rule is that Italians are happiest below 40 degrees latitude.
Carniolan bees are also known for being docile and high honey producers, though less so than Italians in both categories. However, they are much hardier in cooler climates.
(Both of these breeds can be purchased with “hygienic behavior”, which means that the nurse bees have developed a habit of removing mite infested drone larva from the brood chambers. A wonderful adaptation. Ask your bee supplier if they are hygienic bees.)
Nevertheless, when it comes to bee survivability, think of the difference between breeds as less of a hard and fast rule, and more of a tendency. I have seen Italians make it through a rough winter that nearby Carniolans couldn’t weather. I have also seen Carniolans with huge honey production, and Italians with the smallest winter honey stores.
While each colony is going to be unique, it may be best to choose the queen that is best suited for your climate. That way you can give yourself the best odds.