Comparison Costa Mediterranea and NCL Jade / Spirit

The Cabin
The premium balcony cabin we had seemed a tick smaller than the one we'd had before on the Jade. The kids slept in "bunk" beds: the bottom one was the converted couch, the top one folded out of the ceiling. The arrangement worked, but on the Jade they had slept on the remarkably wide sleeper couch near the balcony, with a curtain between that couch and the parents' bed. 
The door to the balcony pushed outward, held by a pretty tough spring which the kids almost couldn't open on their own. Also, to keep the door open, I had to drag the "coffee table" and a chair against it. On the NCL ships, on the other hand, the doors slid open and stayed open in any position you chose - a much better solution. Also, the balcony on the Jade seemed bigger, though I didn't measure it.
The bathroom was functional; however the arrangement wasn't very well thought through. For one thing, the shower had a curtain and was separated from the rest of the bathroom floor by a thin wall about 5cm high. The curtain was too short to go all the way down, however, so when taking a shower, it would billow out at the bottom and water would spray onto the bathroom floor.
Also, the toilet was in the middle of the room, making it impossible for the bathroom to be used if someone was using the toilet. On the NLC ships, both the toilet and the shower are separated from the rest of the bathroom (i.e. the sink) by sliding doors which is much more practical and prevents flooding of the bathroom while showering.
As is frequently the case on these ships, there was a single outlet in the cabin, featuring both European and US sockets. Unfortunately, these were so close that they could only have been used simultaneously by plugging in an extension cord into the US outlet. There was also a dual outlet (US / European) in the bathroom, but this only had power when the light was on.
If you're looking to charge several devices simultaneously, you'll need to bring a multi-outlet to plug in.

The Ship
In general, the ship isn't that much smaller than, say, the NCL Spirit. Despite this, it has fewer cabins and a lot less locations such as bars and restaurants. While the Jade offered several different types of restaurants (bookable for a small uplift per person), the Costa ship offerend only one, the "Medusa Club". We never visited it, but apparently it is a restaurant / club that is quite expensive to eat / drink in. Also, the NCL ships offered more bars, most of them themed, while the Costa ship only has three, two of which have a main thoroughfare going through the middle, which makes them a bit too busy for my taste.
A lot of reviewers commented on the design language of the ship. Personally, the design didn't talk to me, it screamed at me. I've never seen a design that was so mixed and loud on any ship I've visited.
While it screams "VENICE" at you in most parts of the ship, the theater (which is on 3 levels) is decorated with ancient Egyptian pictures and elements. The first time you come into the theater, this comes as a bit of a shock and soothing at once, as it is a much cleaner design.
TThere is venetian glass everywhere (probably made in China), either in bizarre, tentacle-like forms or in the shape of lamps of all types. The restaurant is lit partially by a huge grouping of vase-like frosted lamps, alternating in short and tall. The first thing that pops to mind (mine, anyway) is a 30's Disney animated cartoon where some music plays and the figures pop alternatingly up and down to the beat, in an endless loop of the same 128 frames.
Out of the mouth of each vase comes a colored, sperm-shaped thingamajig, in either blue, red or green. Not sure if the designer was trying to make us think of conception or not, but nothing else popped into my head when I looked at them.

The Food
The food quality is excellent, I was really quite surprised. For dinner, you get thee courses plus desert (and a salad, if you like) and each evening had a different area of Italy as a theme. While I appreciate that Italians probably find that to be quite tantallizing, I much prefer the NCL way, where you have at least some of the food based on the culture that you're currently visiting. No Slavic food to be had while in Croatia, no Greek food while in Greece. Luckily, we generally had a little something while on land to at least get a taste of the region.

Unfortunately, there is no buffet in the evening; while this may be quite ok for adults, it is annoying if you're travelling with younger kids. Instead of getting them fed and off to the kids club, they had to sit through two courses of the adults before getting their dessert. We got this compressed a bit by talking to our waiter, but I really would have hoped for a bit more understanding for kids from an Italian ship.

Breakfast can be had either in the restaurant or the buffet. The buffet restaurant is completely overrun; at times we had to squeeze our way through the masses to try to find a table. Here as with any of the other ships we've been on, you'll find inconsiderate ingrates that decide to block a table for 6 for two people, which doesn't help the situation (only them). While the quality of the buffet breakfast foods is very good, the selection is quite limited. There are different breads and jams in little plastic containers, meats and cheese and fruit. It's plenty to get satiated on, but NCL ships definitely offer a much bigger selection, including eggs in different forms, typical English or US breakfast foods, etc. 

In the restaurant, the situation is more relaxed - there is a buffet, but you can also order special breakfast plates at no extra charge. This is the only way to get eggs for breakfast, or bacon or sausages or pancakes, etc. They also bring coffee and tea to your table, so it is easier going even with kids and - if you can make before the relatively early closing time, definitely to be preferred to buffet.

The Kids Club
Most of what I can say about the Kids Club is straight from our kids. The only "parents" thing to say about the club is that I would have preferred to have less movie times, since all kids are going to sit passively in front of a TV when a movie is on - no matter what language it is in.
Our kids liked the kids club on the Mediterranea a lot, much more than on the NCL ships. They were very happy because the they really liked the activities, felt that the supervisors were all very nice and at least one of them spoke German fluently (the others enough to understand basic needs). On the NCL ships, there was no German-fluent supervision and the level of German understanding was usually extremely basic. I remember one situation where our son wasn't able to communicate that he was unable to open the toilet door (apparently it was stuck) and subsequently wet himself.
On most days, there was a set theme, such as pirate night or fright night and activities during the day were focussed on preparing for a party in the evening, such as making pirate costumes, etc. For the dance party, the supervisors practiced the dance moves with the kids so that they would be a bit more fluid in the evening.
Kids club opened at 9:00h until midnight, including lunch, with a break for dinner where the kids were to be picked up. Since our kids are not very interested in running through ancient cities for the sights at their age, we left them on board on a few days. While this was also possible on the NCL ships, it was considered "Babysitting" between 10:00 and 17:00h, which cost $10 per hour for our two.

On the positive, we have the excellent food quality and the kids club.
On the negative, the list is longer: no buffet for dinner, very limited buffet selection especially during breakfast, no specialty restaurants on the ship (except expensive club), smaller selection of bars, cabin smaller and bathroom impractical.