The last set of header pipes I installed on my RT after the cross over pipes rotted out (not the middle pipe which is replaceable but the nubs on the main header pipes), were the factory pipes. The mufflers are Kiehein and everything seems to be playing well together five years down the line. St.
The basic advantage of stainless over chrome is rust resistance.
The ss alloy is made of iron/chromium/nickel and forms a surface of chromium oxide, which protects the iron from oxidation.
I chose ss over chrome plated steel back in the day because my bikes lived outdoors in New England 24/7/365, and both the chrome plated steel pipes and mufflers seemed to have a lifespan of 1-2 years.
The bikes now live indoors when not being ridden, and they're still using the same ss exhausts acquired back then; the oldest set (pipes/mufflers) has been in use over 40 years and still going strong.
Some folks object to the straw color the ss pipes develop when subjected to the heat of the exhaust, preferring the blue color the heat forms on chrome plated steel; either is fine with me, with the long lifespan of ss being the easy decider, but many folks know they won't hang onto a bike long enough to justify the investment.
So your choice is subjective; your environment/goals/intentions/pocketbook being the factors in choosing.