We just did a Western Med cruise with our five and seven year old kids in October and they very much enjoyed it. As other poster have said, it's important not to overwhelm them and to include enough activities they enjoy. A nice playground or another open space where they can run around can be more fun than some fancy children museum.

Our kids enjoy riding trains/trams/metros, so we made sure we used these where possible. This also saved us money vs. the cruise line tours and shuttles. From Naples, we opted to do Herculaneum rather than Pompeii as it is smaller and closer to the port. The kids absolutely loved to explore the Roman houses and are still talking about them.

In general, we found Italians to be super kid friendly and the food very much in line with our kids tastes.

So, if you adjust the pace to what your kids can handle and include enough activities they like, you will have a great time. Instead of a 10 day or longer cruise, you may want to consider splitting your vacation between a 7 day cruise and a 7 days at a beach resort. This will give you the best of both worlds.