A wood prop does not do well when stored outside for a long time.
Weather will degrade a wood prop faster than a metal prop.
Over torque of the prop bolts can crush the wood fibers.  Of course, you should never over torque any bolt.
You can repitch a metal prop.
If you have a prop strike with a wood prop, the amount of damage to the engine may be less than a metal prop.
A wood prop looks much better than a metal prop.
In some applications, a wood prop is less expensive.
There are many other pros and cons to both props.