I currently use the golflogix app on my phone, but I absolutely HATE having anything besides divot tool and tees in my pocket, so I end up leaving the phone on the cart. That is the primary reason that I believe I would prefer a watch over a handheld device.
With that being said, I deem a watch to be jewelry, and I don't like the idea of wearing ANY jewelry when I'm playing sports (baseball/softball, flag football, basketball, weightlifting, golf, tennis). It drives me crazy. My watch and my wedding band come off. I own some inexpensive beaded necklaces/bracelets (that only look cool lounging on the beach). I haven't worn earrings in nearly a decade, but I would remove those too.
My dad has a Garmin S1 (I think that's the model he has...) and he LOVES IT. I'm going to break down and purchase one in the near future, but I might try wearing a regular watch for a few rounds just to see if it irks me too much