That would depend on the context of the question. Since you are asking the question here in the beginner's forum I'll assume you are talking about props used on trainers or second planes. In that context the biggest drawback to a wood prop is that the are extremely fragile, and will shatter with the least bit of abuse. New pilots will have prop strikes on the run way all the time as they are learning, and these strikes utterly destroy a wood prop. Things such as a not quite so perfect landing, the plane tipping over from turning too sharp, nosing the plane over while taxing, and lifting the tail too far are all common things new pilots do that cause prop strikes. For this reason alone I recommend that new pilots use more durable props, I recommend that they use Master Airscrew props. These props can take quite a bit of abuse and still be functional. After a pilot gets some experience they can start experimenting with other props.

As far as the benefits of wood props, one huge plus on their side is that they don't flex at higher speeds. Fiber filled props such as the Master Airscrew props will flex at higher speeds which actually changes the pitch of the prop.

Hope this helps

Ken