Flight back through the US with a different passport

Hello,

We went to Japan from Brazil with a connection at New York. We used our Brazilian passport with a visa no problem. While in Japan we lost our Passport and our visa along with. We only have a few days until our flight so no time to get another visa.

Here is the question. We also have an EU passport (Dual nationality), would we be able to use that to transit through the US with an ESTA? Or would there be problems because we are using a different passport from the other time?