In flight there is no difference. The airplane moves through a "block" of air, it doesn't care which way the block of air is moving.
I would only assume a difference on landing, a crosswind from the dead side would make de crabbing ( un crabbing?) more difficult.
If I have a choice of runways with equal crosswind I would chose the one with the crosswind on the live side, the tendency to weathervane will assist in aligning the aircraft with the centerline.
But what do I know.....
