My feeling is that, when they ask for both PS and SOP, it would be something like this:
- SOP is to show how your research goals are a match with the program you are applying to.
- PS is to show what you can you bring in terms of personality and life experience.
Some examples. Comparing your research interests with the papers published by faculty should be in your SOP. Stories about leadership or overcoming difficult times shouldn't be in your SOP, but they might be in your PS.