From what I’ve gathered,
Italy has an older population, more people in the high risk age group = more deaths.
A lot of the original cases in India involved Italian tourists, so they’re a bit behind at the moment which explains the lower numbers. Not sure if this is a busy or slow time in India for tourism which is something else that would affect things. The other thing is, a lot of these countries can take extreme measures early on without worrying about backlash. Take a look at Taiwan, they’re doing great and considering their ties with China that seems impossible until you take into account that they can openly track citizens location via their cell phone. India can also heavily restrict movement without worrying about loosing an election.
Last thing, and this isn’t to be rude, but the culture in the states is very individualistic. The numbers are high, because in an individualistic culture people are less likely to sacrifice for the group. The common themes of all these measures to slow the spread are about working together and sacrificing to help others. Cancelling your spring break beach trip, closing your business, and otherwise inconveniencing yourself for others isn’t characteristic of individualistic cultures. Every culture has pros and cons, this is a time when collectivist cultures shine a little brighter.