We know that the impulse is defined by the change in momentum, that is:
Now, we know that we can throw the balls with the same speed and accuracy which means that both balls have the same initial momentum. Now, since the tennis ball will bounce from the wood and the clay ball will stick on it this means that the final momentum of the tennis ball is greater; this means that the change in momentum of the tennis ball will be greater and hence the impulse it exerts on the wood is greater.
Therefore, you should choose the tennis ball.