The reason for choosing cor-ten steel over stainless steel for exterior work is very simple.
Stainless steel is even more expensive than bronze so the material cost to begin with is very high.
Stainless is more difficult to work with so that also adds to the cost in terms of time, effort and sometimes extreme wear on certain tools like cutting tools. Secondly, with few exceptions, too many times folks prefer the stainless to be polished which can add a considerable amount to the overall cost of a piece. Even putting on a brushed finish is expensive, depending on the mill stock. Stainless has some wonderful properties and one of them is the incredible warmth that can be achieved by forging the material, then using the inherent firescale as part of the final finish. It's rare that anyone wants work left in this state though and the brightness, gleam and the polish is what is usually sought out.