Neither for me unless I'm picking up a lot of groceries or something that requires pannier space.

I have a small leather messenger/laptop bag that serves my needs most days. I'll typically throw it in either a front or rear basket depending on where I am (I have my own bikes in a couple of cities and borrow from friends in two others) or strap it on to a rear rack. If necessary I'll throw it over my opposite shoulder (e.g., head through the strap) if I'm on a bike with no basket.

One of my bikes has a crate attached to the rear rack. Another has a front Stecco frame attached rack/basket thats removable.

Some about these racks here: http://localmile.org/city-bikes/

I really dislike riding with a backpack. This due to sweat and general discomfort.