Actually saw this on one of those programmes where a bunch of men do experiments, can't remember the name.
Anyway their conclusion was that they got wetter while running than they did while walking. They wore the same clothes and then weighed them.
The correct answer apparently is that "no-one really knows". It can depend on wind speed and direction as well as body shape. That said, in general you should probably run.
In a series of high tech highly controlled experiments completed at the Met Office college around 30 years ago..... we, my class decided that running was better as you got out the rain quicker....however depending on the intensity of the rain, droplet size and wind strength, however you hit the rain harder than any fall momentum would strike you when standing still... it really disnae matter yer going to get drookit!!
I saw that programme too, Jakep, I think-- Mythbusters maybe? As a non-physicist, I would say running is better, as humans and animals instinctively do it. Probably to get out of the rain quicker.