Davis is an under appreciated program.
In choosing NPI vs. Davis from a practical standpoint, the biggest differences will be lifestyle and research. Davis has a MUCH better work-life balance (shorter hours and less call) compared to NPI. NPI has a MUCH better research portfolio than Davis.
If you have interested in underserved populations, it is more integrated into the Davis program (particularly working with people of color). UCLA does not have a county-focus, except for emergency psych training in intern year. Yes, you can elect to do electives later in your training, but it does not have a county experience embedded as a big part of the training. If you are interested in psychotherapy, Davis also has very strong ties to this, and is quite strong with psychodynamic training.
If you are interested in getting grants for clinical research, UCLA hands down. Also, if you are interested in developing large scale clinical or educational programs, UCLA wins this one, as it is a psych residency with good ties to the wide resources (educational and otherwise) of being nicely integrated with a world class undergraduate institution (Davis is affiliated with UC Davis in name only really, ask the program is in a different city than the undergrad school).
You'll get great training at both programs. If I were me, I'd opt for UCLA if I was hellbent on academic career or loved the idea of living in LA. I'd opt for UC Davis if I was interested in more community-focused training, therapy-bent, or interested in having a healthy non-work lifestyle.