We (2 adults, 2 boys 8 and 2) were on Luminosa this past January out of Venice (off season Adriatic Sea cruise). Will comment on a few specifics below but bottom line we did not like it as much as our only other cruising experience -- RCI Jewel of the Seas on a Caribbean cruise out of San Juan -- but we loved the itinerary and the ship experience and service was enjoyable enough that we are going with Costa again next month on a Norway cruise from Copenhagen.
Paying for pizza and gelato is a little annoying, but was not that big a deal - and at least what you pay for is of quality and perhaps limited access to ice cream is a good thing! Dinner for us was in the Luminosa Club restaurant on deck 10. There was pizza on the dining room kids menu and we ordered one almost every night for our kids to split with whatever else they ordered. It was not as good as the pizza you pay for -- at night they setup the pizza and burgers at the end of where the buffet is and have real pizza ovens vs. whatever they used in the kitchen to make the dinner ones -- but it did the job. Assume the main dining room also has that kids menu. I think we had a set time (early seating) but in practice could go to either seating for dinner.
On RCI we ended up going to the buffet more often than sit down dining -- the buffet on our RCI cruise was great -- but Costa's had more limited options and less for our kids. That plus being able to order the pizza in the dining room had us sitting down for dinner every night except one. Lunch was much easier as they have burgers/chicken/fries near the pool and other options on the buffet (and sometimes this was still open when we got back on the ship after an excursion).
My 8 year old did not enjoy the kids club activities as much as his RCI experience -- but you have to take that on a curve as we had to forcibly remove him from the Jewel kids club every night at 12 or 1 AM. That said, he had a great time on this cruise and as mentioned the clientele (especially on our European cruise) was more international and he made a couple friends from Slovenia and Italy -- they ended up hanging out all over the ship most of the time and have become email pen pals. The Peppa Pig playroom was great for our younger son and even the older boys set themselves up in there.
I actually liked the Luminosa ship layout slightly better than Jewel of the Seas. And I found the ship very clean and the staff helpful (one thing I was worried about before).
Costa is not quite as digital as RCI -- and then add in the international clientele who may like to book things like excursions more in person -- and the front desk can get a little overwhelmed if there are irregular operations. For example our first stop in Bari was shortened drastically due to leaving Venice late, and another day was switched from Kotor to Corfu. If you needed assistance at the reception or excursion desks during the first 2-3 hours after they announced those changes forget about it. One thing that was very helpful is my son and I booked the behind the scenes ship tour and one of the senior customer service folks our tour guide -- she was from the UK and the one who did the English announcements, so for the rest of the cruise if we needed anything she was usually around the front desk area and we could get her assistance if needed.
Not sure how the Caribbean prices stack up, but our two Costa cruises come out to about 70% total price of the RCI cruise and the Celebrity one we have booked next summer (all 4 are 7 days, Grand Suite, 2 adults and 2 kids -- so comparing the base price for room/food, included drink package vs. buying soda/coffee package on RCI, considering what we spent on pizza/gelato, taxes, gratuities). In the future if we find Costa head to head on an itinerary with RCI/Princess we might pay a little more and go with them -- but at this price difference they are fine, especially for the cost to value ratio.