This is at the top here to explain some things about Costa. Costa is a "pan-European cruise line" meaning they cater to the European continent; Italian, French, German, Spanish and British. Like European TV, they present most things like announcements and entertainment, in five languages so everyone understand. Europeans are very used to this, but it seems odd to Americans.
Your waiter will speak English and your menu will be in English. However, the food will cooked for a more European palate which can mean a lot of different things.
The cruise line is owned by Carnival and the ships are identical to Carnival ships in floorplan. The onboard decor is similar to Carnival as well but every ship has a different theme (just like all Carnival ships have different themes) They use the same interior designer, Joe Farcus. If you go on Costa Atlantica you will see it is identical to Carnival Spirit in layout (not decor). If you go on Costa Fortuna you will see it is a mega-ship identical in floorplan to Carnival Conquest.
The staterooms are identical to Carnival, as are the gyms, pools, showrooms, casinos, shops, etc. There are minor differences, some Costa ships have bigger dance floors. The main difference will be the decor, artwork and themes of the ships. They are a little more toned down than Carnival ships but still have the Farcus touch.
The onboard experience is geared to Europeans so they have slightly different entertainment and food than an American style ship. But they are similar to Carnival. The biggest difference will be in the food and entertainment. Expect European style pizza and coffee, and don't be surprised if they have lambchops and beans for breakfast. The pasta is said to be very good, but you might find your steak a little well-done.
If you are an experienced cruiser with high expectations you probably will see drawbacks in a Costa cruise, such as fewer TV channels in English, and tours where English might even be the second language.
Important: keep in mind that the ships present a far more European program when they are sailing in Europe. When they come to the Caribbean, however, they use more of an American model of cruising. Differences: room service choices, tour options, dining times (later in Europe), entertainment.
If you are younger, on a budget, and easy going you will probably enjoy Costa as much as any cruise line. Its just a matter of what you are used to and your expectations.
Experienced cruisers have different expectations, for younger ones it's a cruise and any cruise is great.