Having sat down and worked it out, the answer does all depend on the angle of the rain. In vertical rain, or a headwind, or a sidewind, then you hit less water the faster you go. In a tailwind, it's sometimes possible to do better if you can match the horizontal component of the velocity of the rain. The terminal velocity of raindrops is about 20mph, says Wikipedia, so, if the rain is coming down at an angle of arctan(3/20) or 8.5 degrees to the vertical, and you walk at 3mph, you get less wet than running -- though this does assume that your plan area is much less than your frontal area.

Of course in practice there are other factors -- the relative porosity of various parts of clothing, wind-drying effects caused by running, and, for those who remember Glastonbury 2004, the fact that once you're soaking wet you aren't getting any wetter however fast or slow you go.

Peter