I'd say it is largely a matter of personal preference. Just don't use drywall screws as they are fairly brittle. But normal wood screws or pan head screws will both do the job. Presumably, most people don't want to see a screw head in their face frame when they open the door, so I'd think pan head wouldn't normally be used, but that doesn't mean it is a bad choice. In my cabinets, I used normal wood screws, countersunk so the heads are flush with the surface of the faceframe. I think I used 3" screws so I got about an inch of screw into the adjoining faceframe.