There are some backpacks that resemble two strap messenger bags so the lines can get blurred a little. One big advantage as other people have said is that you can easily swing a messenger bag around to the front and get at the contents without taking it off.

A couple of other advantages you can find in some backpacks but are fairly universal in messenger bags, is weatherproofness and a huge flap which makes it easier to pack large and oddly shaped items.

Again, there are lots of different kinds of backpacks so this isn't a problem with all of them, but on a road bike the top can occasionally hit the back of my helmet if they ride too high.

With both backpacks and messenger bags, spending some extra money to get better quality will make you a lot happier in the end. For example, don't buy a messenger bag without a cross strap. So many people that have tried messenger bags and complained that they moved around on them didn't get ones with a cross strap.