I find the up side to messenger bags is that my back is not covered up as much as it is when wearing a backpack, so it is more comfortable in hot weather.
Also, I can move the bag around so it is not just resting on my spine. I find backpacks to be uncomfortable when stretched out on the bike. A messenger bag is in contact with much less of the back. I can choose what part of the back it is in contact with as well as move it around to vary where it sits more easily.
When I use a backpack I always end up loosening one strap and slinging it off one side or the other, basically trying to get the least contact with my back and spine.
I have not had any leakage issues or anything falling out of the bag.
You do have to make sure you have it closed up enough to contain whatever you are carrying however.
It's also nice to be able to put something oversized in the bag - a box or whatever - and be able to transport it where ever it needs to go. In this application you can just leave the flap open or use the flap and straps to hold the box or parcel in place on the outside of the bag. I've carried some very bizarre items in this fashion.
I find messenger bags somewhat easier to rummage in while still attached to the body than backpacks.
The downside is in carrying really heavy loads. Quite allot of pressure can be put on the shoulder carrying the load.