Personally I would say the Bihar. I tried on the leather version in Von Maur a couple of weeks ago and thought it was very comfy. The Shimia is 20" W which is really big in my opinion. Unless of course you like big bags, which I don't.
LunaBoston has modeling shots of both, based upon those and the strap drop, I'd say that the Bihar is a better shoulder bag if you want to be able to wear it over your shoulder in a winter coat.
I have the Bihar and it fits comfortably over the shoulder. I wore it over the shoulder with sweatshirt hoodies and a thin leather jacket and it's okay. I don't know about heavy winter coats though as I haven't wore a heavy coat with it yet.