The rubber ball will 'typically' be less dense than a wooden ball of the same size or
If we assume the wooden ball is hardwood like maple and the rubber ball is foamed rubber and not like a hard rubber lacrosse ball, the given statement would be correct.
The reason is the difference in momentum between the two balls. The momentum of the moving ball is related to its mass, and its mass is related to its density.
Density is defined as the mass of the ball distributed over its volume. In this case the density of the (soft) rubber ball is less than that of the (hard) wooden ball.
That means the mass of the rubber ball is again less than that of the wooden ball.
Since both of these balls are moving, their motion results in a stored energy called momentum. Momentum is the result of the mass of the ball times its velocity. Then, from above, we see that the momentum of the rubber ball is less than that of the wooden ball.
Under these conditions, I would rather catch the rubber ball than the wooden ball.
If the rubber ball were to be a lacrosse ball, and the wooden ball made of balsa wood, then we would have the opposite result.