in any BPL theoritical ideal perfect situation the rain will be falling directly straight down. and of course the wind will be neutral direction or zero. so now that we have established conditions that can not actually exist, it's time for a BPL discussion ! that this discussion may eventually invoke religion, name calling, satire, and economics .. it's a foregone conclusion.
here we go :
let us assume that a pair of un-gendered folks named Runner and Walker are going travel from A to B over distance x~y, and it will be raining that nice statistically perfect precipitation so common on the internet.
Runner and Walker, being a species of "folks" are conveniently shaped as upright rectangular boxes, not unlike small phone booths.
because of their shape, and the ideal rain conditions, during their travels from X to Y in the rain, R and W will get wet only on their top and front surfaces.
it gets good here ..
the volume of area swept by the identical sized R and W in their travel will be the same.
at any given moment, the amount of rain in this volume remains constant.
both R and W will both sweep this volume and in doing so absorb the amount of water it contains on their front surfaces. R will sweep it faster than W, but the water amount will still be the same.
HOWEVER, W takes longer than R, so it (no gender.. remember), because of the longer duration of exposure, will be exposed to a greater amount of rain impacting it's upper surface.
we can all know from this astute analysis of the situation, that R will stay dryer than W.
thusly, the correct answer to the question is "all other things being equal .. Run."
you're welcome ..