Left shoulder for me. I'm right handed so it's easier for me when I reach into my bag for stuff. Feels weird fo me if I carry it on my right. But when it comes to the handheld bags, I use both arms.
Left shoulder--I'm right handed but the bags ALWAYS fall off that shoulder! So, it's the left for me! I also carry handbags on the left so my right hand stays free...
...this is a good question!! I'm really liking this thread!