There is no question that the wider grip feels better. I am a wide guy so the torque on my elbows is not pleasant with an inside grip. There is no question for me that I am stronger from that position. That said, I have been told the opposite is true for other guys who are very good curlers. If you are curling your body weight, I would never listen to someone who said you are doing it "wrong".
As I stated earlier, I think one of the most important areas to train, and train hard, is the front delts. When I curl heavy weight in comp. I try and drive my elbows up. This is a front delt movement.
One exercise I do religiously on shoulder day is seated, reversed grip (palms inward)front overhead press on a Smith Machine. I go as heavy as I can stand it for sets of 6.