The primary advantage of a wooden soda crate or similar is that it would look neato.

I've used a plastic milk crate on a rear rack. It's very convenient, especially if the sides are high enough to keep things from bouncing out. Just drop in your stuff and go. However, my wife thought I looked like a homeless person and got me a nice tail bag.

The advantages of a wire or plastic crate rather than wood is that they are more durable and have less aerodynamic drag.

Panniers don't quite have the same toss-and-go ease, you need to pack them. They have the following advantages. They close, keeping the rain out of your bag and keeping stuff contained in a wreck. They are carried lower and so they have less effect on the handling - a crate with a jug of milk can give you a tank-slapper. Expandable versions are less obtrusive when not in use.