The answer is a complex mathematical equation that takes into account the rate of rainfall, the volume of rain per cubic meter and the rate of running or walking.The answer will change according to these variable parameters.
For example, if walking is better (less wet) than running, that does not mean that walking even slower is even better because then standing still would be the driest option and that cannot be. From the other side, even if one would run at the speed of light, he would catch all the drops available at that instant and still get wet.
A very famous question with a not-so-simple solution.