Various prop materials will flex when torqued. That produces a somewhat ineffective prop. From what I understand, some of the better wooden props will flex less than the plastic or plastic composite materials. But, they are more delicate than the plastic composite props, meaning that they can shatter much easier than a plastic composite prop.
Then there are the carbon composite props that are probably the best around, but much more expensive than what we get off the shelf with wooden or plastic composite materials.
I have gotten into the habit of using APC plastic composite props only because they were easy to obtain (the LHS has a very good stock of varying sizes) and inexpensive. When I was in training, I was breaking one or two a day for a while

. So, inexpensive was the key and I bought them by the dozen
I'm sure that there will be more information forthcoming in subsequent replies, though... some more technical and others more emotional...
CGr.