I'm looking at the Rapha Mens pro team winter jacket. I'm between sizes. Rapha recommends Small for 37" chest and Medium for a 39" chest. My chest measures 38" I'm 5'9" and 158lbs.

Does Rapha sizing run small or big?

Rapha jacket

Medium
I’m 41” and go for Large from Rapha
and I also only ever buy from them at sale time 😁

Chest 39"
Height 6'
Weight 175

Wear size XL in Core winter jacket. It's comfy with a long sleeve jersey, but not flappy or loose. Pro Team fits more snug.

Good tip. I might take a trip to the rapha store in Manhattan to try it on.

I have that jacket, and it runs very snug: I'm normally a Large in Rapha tops, and the XL jacket is very snug: I can wear it over a thin baselayer in temps down to about 45, and over a thick baselayer down to about 40 degrees. No way could I wear it over a baselayer and a jersey, but I don't think that's the intended use for it anyway. It's designed to be a rather minimalist and snug outer layer for cool/cold weather. I just think of it as a very warm and somewhat wind resistant jersey.

By the way, my chest size is the same as yours: about 38" currently, though my shoulders are rather broad. I couldn't even fit into the Large jacket, and find it hilarious that they recommend a Medium for my chest size.

tl;dr: size up.

I take back my Medium recommendation

To be fair, if you mostly buy from Rapha's other product lines, you may not need to size up. I own a whole bunch of jerseys from the Classic line, and they're all Large. (One might even be a medium.) But the Pro Team line sizing is a good bit snugger.

Maybe no help but...
I just got a used Rapha Pro Team Rain jacket in XL. Chest size 43.5" and wide shoulders. Thankfully I'm losing weight (at 195 now, 5' 9.5") because it is just on the margin of wearable over a jersey.

To be fair, this is their early model of the jacket, with modern ones rumored to be cut snugger. Personally, without trying it on I would size up two sizes from normal mortal clothing.