The practical difference between the two is that steel stoves heat up faster and distribute heat to the room much faster, whereas cast iron, the traditional material for stove construction, because it is much heavier, tends to take longer to build up heat and distribute it to the room. However, this mass of metal also has the advantage of being a significant heat sink for the slow release of gentle heat after the stove's fire has gone out - but only if the stove has been at operating temperature for a good hour or so. A steel-bodied stove will still do this, but it won't hold heat for quite as long. So essentially it's a lifestyle choice - if you need fast heat, choose steel, and if you want longer lasting heat, say into the wee hours of the morning, choose cast iron.
14 October, 2020
If you're talking about a good quality steel-bodied stove versus a good quality cast iron stove, it really doesn't matter, provided the stove is used according to the manufacturer's instructions. Poor quality cast iron stoves have a reputation for cracking and poor quality steel bodied stoves have a reputation for warping.