Unless there's some new breakthroughs I'm unaware of stainless steel doesn't contain aluminum, nickel and chromium are the major alloying metals. Blued steel barrels are made from various alloys of ferrous steel, generically called "carbon" steel, "chrome moly" or simply "moly" steel because of the alloying elements.
A chrome lined barrel is different, it's essentially a very thin layer of pure chrome that's plated to the inside of the barrel after it's made, with rare exceptions this is only done to military rifles. Military barrels are chromed for a number of reasons, barrel life being one of them but more precisely to protect the barrel from damage during cleaning. Anyone who's done a hitch can tell ya how often military rifles are cleaned and the effort expended getting the bores beyond spotless. This constant over-cleaning combined with Uncle Sam's POS jointed cleaning rods has ruined more barrels than any other single cause.
A stainless barrel will last longer. Exactly how long is hard to say but some of the number I've heard from Service Rifle shooters is a conventional barrel might be good for 5 thousand rounds, stainless for 6 maybe 7. Chrome lined barrels will last about as long as stainless but aren't used for competition shooting because they are typically less accurate and no civilian makers offer chrome lined barrels. And though stainless barrels have a longer life, because they can better tolerate high flame temperatures, they are more easily damaged because they are not as hard as blue steeled barrels and therefore more readily damaged due to improper cleaning. -- Kernel
