Fiberglass shafts are more flexible and slightly heavier than the other shaft options. Especially the longer fiberglass batons tend to have more "spring" in the tip. One advantage of a more flexible shaft is that it will bend farther before it breaks. If you catch a fiberglass baton on the edge of your podium, chances are pretty good that it will bend far enough that it will not break. Fiberglass is white through and through, so if you tap the shaft it will always look white. However, the more you tap, the more the fibers in the fiberglass start to break apart. Once these fibers are broken, they can give you slivers if you run your hand along the worn shaft (so I don't recommend tapping your stand).
Graphite shafts are almost black underneath a coating of brilliant white paint. If you tap the podium with a graphite shaft, you will eventually wear through the white paint, but fortunately it will not give you slivers. Graphite is stiffer and lighter than fiberglass. If you flick the tip down to a vigorous downbeat, it tends to stay where you put it with minimal vibration. A baton with a graphite shaft is very nimble and moves with very little resistance.
I custom build my wood shafts from Baltic birch and then brush on multiple coats of clear wood lacquer in order to give them a nice shine. The natural tan color of the birch provides a nice visual contrast against a white background. The wood shafts are lighter weight and slightly thicker than my fiberglass or graphite shafts. The biggest disadvantage of wood shafts is that they are somewhat fragile. They break much easier than the other shaft options and they can warp over time (especially if they are subjected to abrupt changes in temperature or humidity).