The level of competition that you describe for the acting academies in Italy is lower than the level of competition for admission to top acting programs in the US as an international applicant. That is to say, if you apply to both, the chance of getting a spot in Italy will be better.
What is your family truly ready, willing, and able to pay for your education? Do you have a figure in US dollars? Think about that. In the end where you can attend will be determined by cost.
I was going to recommend that you also post in the theater/drama forum, but I see that you found it. Spend some time reading through different threads there for more ideas.