We sailed the Med. on the Concordia with myself, d/h and our 2 kids ages 6 and 8 at the time a little over a year ago. Our issues were more along the lines of food quality and customer service quality, and passenger behavior.
We usually sail Carnival or NCL, we've also sailed RCCL as well, just so you get an idea of what we are accustomed to. We found the food to be subpar, below what you'd find on the cruise lines we've sailed on before. In some cases they would list a halibut on the menu, and they would serve a thin filet of something resembling a tilapia, which are completely different in texture, taste, and one comes from salt water, the other fresh and when you ask them what fish it is they become very angry that you dare to question their substitution, of course it is halibut
The surcharge restaurant on the Concordia is billed as a Michelin star ranked venue with a special cooking technique involving banana leaves cooked in sugar or something to that effect, when we arrived there for our meal, none of that existed and the food was along the same lines as what you might find in the main dining rooms on NCL and Carnival. Steaks, fish etc... and it was just OK, and not what was advertised. On port mornings we went to the dining room to have breakfast and they had converted the main dining room into a buffet... I asked the Maitre D if I could order from the menu and he put a plate in my hand and said eat at the buffet...it's good enough, when I objected to that he started getting rude and we walked out.
Don't get me wrong no one starved, but we kept wishing we had booked on a different cruiseline and regretted our decision to cruise with Costa. You will likely observe the rudeness of many passengers and crew as well. I have no idea why certain people think a line to the reception desk is for everyone but them, and become quite nasty when you point out where the end of the line is when they decide to cut in front of you or you are in the back of an elevator when it arrives at your floor, no matter how many times you say pardon moi or excuse me, or anything the people will not let you off.
I really doubt I would sail Costa again based on our experiences. I can say the Kid's Club was fine, the only issues they had there were the same issues we observed was the rude children, who were probably the offspring of the same rude adults on board. The ports were great, they often cancelled english speaking excursions due to a shortage of english speaking passengers. The room stewards were wonderful though and couldn't do enough for us.
Going to the spa was a comical and culturally enriching experience. I got to know a few folks from Canada and the U.S. on board and we would sit in the Thallassotherapy tub and watch people from other parts of the world come in and soak, some wore their underwear, some wore very transparent, see through garments, others not so much.
I am sure we'll do another cruise in the Med someday but I know it will be with a more mainstream cruise line.