Anyone who knows knife blade steels knows that carbon steel will (depending on other ingredients) hold an edge better, but for firearms, make mine stainless.
Stainless steel resists gas and flame cutting much better than carbon steel. It absorbs blast better and yes, resists corrosion.
In the early days, stainless gauled against stainless, requiring heavy, sticky lubes to work. Now they work very well with each other with almost no lube.
The only downside to stainless is that it tends to reflect more, a problem for hunters. For homeowners, not so much a problem. I've taken stainless and blued guns into dark rooms, and stainless guns did not stand out as I'd originally thought.
For regular shooting, either will do well. For magnum shooters, go stainless. Hard chrome is good for 1) wear and tear and 2) resisting corrosion and scratches. Parts that are hard chromed wear phemenonly, especially on small moving parts like hands/pawls.