anecdotally, the advantages I personally see.

I used to use a regular backpack, and my back often hurt after my commute.

I switched to a messenger bag, and never have had my back hurt since, and it just feels *so* much more comfortable.

The second advantage it its much easier for me to get stuff like my lock/lights/etc out of my back quickly, just swing it around in front of me, and swing it back.

Thirdly is its waterproof (although some backpacks are too, not the ones i had).

fourthly is, its more fashionable, and more a part of urban bike culture.

the main disadvantage is just not as many pockets and stuff as a backpack.

I am not a messenger, but use my bike as my only form of transportation, so groceries, laptop, everything goes in the bag everywhere.