The NEXUS program is a joint US-Canada program meant for travellers transiting between Canada and the US. Global Entry is an American program for easing entry into the United States. Neither program has anything to do with Italy. So the answer to your question is: “Don’t bring your NEXUS Card to Italy.”
The US has programs similar to NEXUS with other countries, but Italy is not one of them. You should just bring your passports on your trip to Italy.