If you’re speaking of great quality steel stove versus quality cast iron stoves then, giving that the stove is used directly with the manufacturer’s intended instructions, it shouldn’t really matter. Poor quality cast iron stoves have well known reputation for cracking under high temperature exposure, that as well as poor quality steel wood burning stoves have a reputation for warping when at high temperatures. The difference between the two types of stoves are that steel wood burning stoves heat up quicker and expel more heat to the room it is in much faster than cast iron. In which is the traditional material for wood burning stove building, since it is much heavier than steel and provides a greater mass of the metal, it tends to take longer to build up heat and expel it to the room.
In history steel was regarded once as a poor material for wood burning stove manufacturing, this would result in warped steel stoves. Steel quality however has now greatly improved so there really is not that much difference between cast iron anymore. In some cases cast iron wood burning stoves are built more heavily and more sturdy than their counterparts steel stoves, and in some cases may have the quality edge.
Cast iron stoves, which are known to be generally heavier than steel bodied stoves, they have the advantage that the mass of the metal in the body of the stove acts like a heat storage radiator dispensing the heat stored into the room for few hours after the fire been expelled. A steel bodied stove will do this too but it won’t retain its heat for quite as long. So, essentially it’s a lifestyle choice – if you need fast heat then chooses steel and if you want longer lasting heat, say overnight, then choose cast iron.