Yes, I definitely do prefer a bag that goes over my shoulder.
I find these far more convenient as if you sling it right across your body, you have always two hands to do what you want with, especially when shopping.
I find bags with short straps are a nuisance as you only have one hand to "operate" with, so I have very few hand held bags and those I have are evening bags which I no longer use.
Handles are such a pain . . . you always end up with them up in the crook of your elbow and it hurts and you knock things over etc. . . like a guided missile. Ah, happy days, shopping with mother and her handbag. Haha.