More calories, more variety, more cheap GMO tomatoes in their store-bought sauces and ketchup (European aristocrats thought tomatoes were poisonous -- hah, hah, funny right? Funny like scurvy, a constant scourge of all social classes back then), cleaner drinking water (!), less food-borne pathogens, less periodic bouts of famine, less dependence on seasonal variation in available food sources, hot and cold food available on demand.
Your points about health are reasonable, but I don't think the modern diet really has more variety than the Medieval aristocrat's did. The kinds of meals eaten by the upper classes back then would still be considered extremely luxurious today.
A middle class person today can if they choose have a much more varied diet than anyone could in medieval times. Even as recently as the 19th century it was an extraordinary luxury in northern Europe to have fresh fruit or vegetables in the winter, for example.
And of course medieval Europe did not have any of the species they later got from the Americas: no potatoes, peppers, corn, tomatoes. There was no coffee or tea or chocolate either. And no ocean fish unless you lived close to the sea.
If you were a rich person in medieval times you could basically have a much roast beef as you wanted. (That was apparently Charlemagne's undoing.)
Just consider variety in terms of ethnic foods. No Medieval aristocrat had easy access to Indian/Chinese/Thai/Japanese/Korean/Mexican/Greek/Ethiopian/French/Italian/Brazilian/Cajun/Cuban/Vietnamese/Taiwanese food, all of which are available within a half hour drive from my house.