I have problems with my neck and several times a year I put myself out of commission when doing the barbell overhead press. I believe its associated with the awkward forward movement of the head and neck once the bar clears the top of my head. Will I see the same benefit if I substitute a dumbbell shoulder press for the barbell press? What are the pros and cons of switching? My theory is that I will have less problems because I won't have to move my head as much. Thx.

There is no con unless you are training for an event where you have to barbell overhead press.

Dumbbell work should make you improve faster since each arm has to work independently and you can't rely on your dominant arm to pick up the slack.

The only issue is sometimes being able to get enough weight into a pressing position. With a barbell, you can use a rack. A spotter to help you goes a long way to alleviate this.