Originally Posted by Silver Fox

I would take both passports, I think that when you enter your passport that has the "old" ESTA it will pop-up your flight details as that is associated with the advance passenger information you will have supplied. If you put in your "new" passport and ESTA it will likely say "huh?" and not find the flight details. As for filling in the ESTA for your new passport all you can do is fill in (or scan) the details from it and enter them exactly as they are, there is a part where you have to say if you have other passports or "alias", and that is where I would put it. On the basis, I don't think there is anywhere else to put it. But as someone said, whatever you do don't lie or try to be clever, just answer what they put in front of you honestly and all will be fine.

And yes, having to endure the first time ESTA, and in fact, US immigration (without GE), is like a step back in time.