travel to US

Hello,

I have a 10-year multiple entry visa to the US on a passport which has expired. My country of origin has recently been included in Visa Waiver Program (at the time I got the visa it was not, obviously)

In order to travel to the US now, I think I have 2 options:

1. Travel with my old and new passports, showing the old one for the visa and the new one as a valid passport. In this case, should I still fill out an ESTA or does my old visa replace the need for the ESTA?
2. Forget the old passport with the visa and just use the new one and fill out an ESTA

Which is the better option?

TIA