having experience with the twins of both ships (MSC Opera and Costa Atlantica) i'd say, it is mainly a question of taste.
If you love the glittering, shining style of the C. Med., which is strongly inspired by Costa's American mother company Carnival, and reminds me of a huge floating Las- Vegas- style Casino Resort (and is to me not "Italian Style" at all), you might be disappointed by the conservative, yet very elegant art- deco inspired interior of the MSC Lirica. Those used to the giant vessels of the "new" Costa might find her boring, but to me, she is much more ship- style, which i enjoy. In case you love the Costa decor, you can cancel your reservation and change to the Costa Magica with an almost identical interior (to the Med.) and itinerary
In nearly all other respects, i found MSC superior to Costa, especially when it comes to service, value for money and food (we had surprisingly excellent genuine italian gourmet food on the MSC Opera, whereas the food on Costa was much more "all- european" style, and the preparation was sometimes mediocre). But nowadays it is hard to make any prediction on food, as the market changes so fast.
Negative aspects of the Lirica versus the Mediterranea are the smaller size of the cabins (13 square meters vs. 16), the modest size of the self- service restaurant (i'd prefer the service restaurant instead) and the lack of an indoor pool.
Think it over, and decide. I would stick to MSC, but my personal taste is, that i love cruising with a typical italian signature. Others prefer a more all- european style- those will probably be happier on Costa.