I used to use a backpack. A few years ago I bought the biggest messenger bag I could find which was maybe my mistake because I stuff it full. There's only one shoulder strap but there's another strap that crosses your front to secure it so it doesn't shift. As far as comfort goes, I don't find the single shoulder strap to be a problem. When I'm riding, the weight is on my back and not on my shoulders.

The advantage over a backpack is that I can easily sling it over my head and shoulder and not worry about it falling off. You can carry a backpack with just one strap but you need to keep a hand on it. A messenger bag can be worn on the back, side, or slid around in front of me (without taking it off) if I'm sitting down on bus or train.