There is a lot of good information in this thread. Of course, different personal circumstances will sometimes lead to different answers.
For example, children born abroad to a Filipino citizen (father or mother) are considered ‘natural-born’ citizens. If the Filipino parent lost their Philippine citizenship before the child was born, but then re-acquired Filipino citizenship before the child reaches 18, the child is a Philippine citizen.
There used to be a lot of different passport combinations people used to enter and leave different countries, and most of the time it did not make much difference as long as the US citizen used the US passport when entering the US.
This has changed in recent years (at least ‘recent’ to me!) so now it is important to match the passport info on the airline ticket with the passport to be used when entering the US. Recall that all the behind-the-scenes security checks are performed pre-arrival based on the passenger manifest and identifier data provided by the airline. Boarding with one passport and entering with another may lead to some additional questions upon entry.
Also, I wonder if there have been some technological improvements the last couple of years in the Philippine entry/exit data records. Twice at entry I’ve had them swipe my passport, then ask if my wife was traveling with me, and once the officer politely engaged me in a conversation about one of my two-day trips that happened years ago on a different (now expired) passport!