No, you will NOT be allowed enter the US using your visa on the expired passport.
Although the US does allow entry using a visa on an expired passport, this is only allowed when the personal details - including nationality - are the same on both passports. Or put another way, the passports must both be from the same country.
Without a valid visa the airline you are flying will not allow you to board your flight to the US.
From https://www.ustraveldocs.com/au/au-gen-faq.asp#qlistgen8 :
Q.8 My passport has expired, but the U.S. visa in it is still valid.
Do I need to apply for a new visa?
Also, the name and other personal data must be the same in both passports, and both passports must be from the same country and of the same type (i.e., both tourist passports and both diplomatic passports).
(ustraveldocs.com is run by CGI Federal, the company responsible for processing US visas in most countries around the world. Whilst not technically an official US website, the information on it is as close to official as you can get)