Many older guns were just fine with steel shot. MOST new guns made since it became required are designed for it. Many older guns, especially doubles had very thin steel in the barrels to keep weight down. Those are the ones most likely to cause problems, especially ones with more tight chokes. Most common older pumps etc are fine as long as they are not full choke, but I'd check if in doubt.
Steel is more expensive than lead, but much cheaper than the other non-toxic options. Many of the other non-toxic loads duplicate lead better and most are safe even in older guns. I have a 1930's era double I hunt duck hunt with on occasion. It only gets Bismuth shot. I cannot afford to use it all the time.
Early steel had issues, newer shells are much improved. Lead is lighter, so you need to move up about 2 sizes to get the same amount of weight in each pellet. If #4 lead is a good choice, then #2 steel is about equal in performance. But when you move up to a larger shot size, there are fewer pellets in each shell. This is why 3" and 3.5" shells are more common.
A 3" #2 steel shot shell is about equal performance wise to a 2 3/4" #4 lead shell.
Steel also patterns tighter. An IC choke will shoot steel into roughly the same pattern as a Modified choke will shoot lead. You should never use steel shot in a full choke designed for lead. And there is no need since a modified choke will shoot pretty tight steel shot patterns. I almost always use IC with steel since it gives me the best patterns. Modified with steel is just too tight.
Since steel is lighter, it has slightly less recoil. A 3" lead shell will kick pretty hard. A 3" steel shell has about the same payload as 2 3/4" lead and recoils about the same.