Obviously the stainless barrels are more corrosion resistant compared to the chrome moly barrels but with proper care the blued steel, with a quality blueing job is pretty weather proof.
I much prefer the stainless because of its longer throat life compared to chrome moly. Dan Lilja states that his SS barrels offer 25% longer accuracy life then his chrome moly barrels and from what I have seen, I would say that is true.
For someone dropping $1500-2500 on a custom rifle
, 25% longer barrel life is a decent about more of shooting.
Accuracy wise, I have never seen any evidence that one type of steel is more accurate then the other.
Stainless Steel barrel bores can be held to slightly tighter tolerances but we are talking in the 0.0002" range over the length of the bore compared to 0.0001" for the stainless. Really nothing in the real world.