Cast Iron is cheap to make in a mold, often bolted together if made in sections and if so, may leak air at the seams, has reasonable fire resistance, can eventually crack from thermal cycling. Often made to look "retro".
Steel is easy to make air-tight, requires metal brakes to fold the steel plate into shape, and the seams need to be welded. The firebox will be lined with firebrick to protect the steel from overheating and serves as thermal mass and also increases the firebox temperatures which if combined with secondary air-intake, will help completely burn all combustibles.
Ceramic/Soap Stone stoves essentially dispense with the steel shell, have thick walls for thermal mass and fire resistance.
The major difference in the way steel and ceramic stoves work is the thermal mass that a ceramic stove can have. Steel stoves are efficient at getting the heat out fairly immediately and drive you out of the room in doing so. There is temperature variation.
Ceramic stoves take a lot longer time to warm up, but once heated, serve as a thermal reservoir that absorbs and releases heat over time, leading to more even temperatures. If you let the fire go out, it will take longer to start delivering heat than either Cast Iron or Steel stoves.
Pay attention to the instruction manuals as there are differences in firing methods and also pay attention to not over-firing any of them.
So, it boils down to "Do you want quicker heating or are patient to have more even temperature delivered over time?"