I guess I try and keep it simple so the fewest questions are asked of me and generally don't want to produce anything that could confuse a check in agent, such as two passports. Besides, a check in agent is not, IMHO, an official CBP agent. If the US wants to do emigration checks like most countries, fine, I'll show you the US passport. But some minimum wage contract check in agent for the airline? No. I understand the argument that they are the first line of CBP checks, but disagree with it.

What's real fun is doing a routing like DUB-LHR-EWR, checking in/leaving DUB on the EI passport (as required by EI law), then showing up at LHR for the second round of checks with a US passport. "Sir, didn't you check in with an EI passport?" Cue cavity search...