Great points Rocco and iron, some people do partials by stopping at ear level, but yup they miss out on the full stretch. I think full stretch and full contraction should be something one pays very close attention. I also perform both lifts. Sometimes I do both and I may also perform one over the other ad part of varying my workouts to prevent staleness. Press behind neck pay special attention. I'm sure the research hounds will chime in because many physiologists and trainers caution against performing this move as it places the rotator cuff in a very weak position. However, I love press behind neck for my main shoulder exercise. If I go heavy I use smith machine , if I don't have a spot. Dim bells one can actually stretch even further at the bottom, plus the benefit of balancing the single dumbbell .
One of my favorite shoulder variations to increase the burn is to pump out 8-10 reps on smith machine press behind neck , then quickly before my delta recover, I jump on the bench and do upright rows , utilizing the biceps that are still fresh to further work my delta. I use a flat bench at smith machine to work my core- no belt iron insanity ha ha ha for both exercises.