Stainless barrels don't suffer the same confusion as carbon steel AR barrels. There are four "tiers" of stainless steel barrels: 410, 416, 416R, and 17-4 PH.
Advantages of Stainless vs. Carbon Steel
There are two major advantages to picking a stainless barrel over a carbon steel barrel: First, it'll provide better corrosion resistance with better accuracy. A carbon-steel barrel could last longer if it has a chrome-lined finish, but chrome-lining affects rifling and shot placement. Second, a stainless barrel will provide better "toughness". Stainless barrels are more resistant to heat and abrasion than carbon steel. All other factors being perfectly equal, a stainless barrel will last longer than a carbon steel barrel.