Both JFK and Newark run nonstops to Rome, and the fare difference between them is often larger than the difference between airlines.
JFK is served by Delta, American and ITA Airways on this route, and generally offers the most departure times. If you’re in Brooklyn, Queens or Long Island, it’s the obvious choice.
Newark is United’s hub, and their nonstop to Rome runs year-round. For anyone in New Jersey, Manhattan’s west side, or Westchester, Newark is frequently both closer and cheaper.
LaGuardia does not fly to Europe. If a search returns an LGA itinerary to Rome, it involves a domestic connection first, usually adding four hours or more for no saving.
Always search both JFK and Newark before booking. Setting your origin to “New York (all airports)” catches both, and the gap between them can be $150 or more on the same dates.