This is more a question on how realistic/detailed they made it, not entirely about the way it looks. I would also like to add that I haven't yet played the game.
What kind of rain does it have, and how does it work? I know I'm hoping for a lot, but do physics objects (Stuff you can grab. Bodies, long planks, etc.) block the rain? I doubt it, but do droplets drip off of surfaces? Do puddles form? Do surfaces not hit by rain not get the shine effect on the material? Does the texture change from rain depend on the material (Concrete doesn't get shiny, but metal does)? Does rain affect the player model (metal armor shine, cloth armor drip)? Do bodies of water ripple and bubble? Do streams form in gutters? If so, do they get blocked off by physics objects? I know in the past it has been simply a visual effect. Kind of an overlay. Is rain different now?
These are probably crazy questions. Walking home in the rain got me to thinking about accurate models of rain and dynamic weather, and as a particularly large piece of hail hit my head I got the funny idea that Fallout 4 might feature some of it. This is the kind of thing I'd expect from a high quality animated film. I'm sure all of this would be absolutely insane to render. Rendering liquids in Blender has always killed my computer, so I can't imagine what rendering half of this stuff in real time would do.
I suppose this one is a simpler one: Does wind exist?
Does it affect physics objects? Does it affect the environment? Is it blocked by the environment? Is it blocked by large physics objects? Does wind affect weather patterns? Does it affect bodies of water?