We recently had a thread on medieval versions of lasagna that might interest you.

The basic idea of stuffed pasta (ravioli, tortellini) existed as well. The famous difference, of course, would be the lack of tomatoes and tomato-based sauces.

Here's a 14C illustration of noodle-making. The text it illustrates is a Latin translation of an Arabic medical work saying that pasta is good for the throat and chest.

It's hard to pinpoint the food of the poor classes in ancient and medieval society. We can speculate what they ate based on the foods available, but not much else.

We know a lot more of what the rich ate however. And in relation to your question, the cuisine of the rich Romans, derived from Apicus, differs quite a bit from Medieval Italian cuisine. I'll explain the two largest differences I found.

Eggs. One of the key features of Medieval Italian cuisine is eggs, they are found in hundreds of recipes. Italian cuisine mentioned in French, English and German cookbooks of the time often call it "Style Lombardy" and almost every time mentions eggs as an ingredient.

The second major difference is spices. While Romans did have access to spices at the time, such as pepper, it was exorbitantly expensive to Romans. Much more expensive than for a Medieval nobleman. This made spices less common in Roman cuisine, even for the rich.