Cast iron wood burners can be radiant, combustion or circulating stoves. Single-wall cast iron burners heat with radiation -- the heat radiates off the stove wall into the surrounding space. The surface of such a stove gets extremely hot, making it unsuitable for homes with pets or children. Circulating wood burners have double-wall construction, and the heated air between the walls vents out to warm the area. Combustion wood burners burn hotter than other types; you can open the door while the fire is lit, adding oxygen to the flames.
Brick-lined steel has a steel exterior and an inner chamber of firebricks. The steel exterior is not as decorative as cast iron, but the bricks inside the steel exterior will let you burn a hotter fire. The brick lining insulates the stove, holding heat inside for radiation through the door or with convection currents. The exterior of a brick-lined wood-burning stove does not get as hot as cast iron because the masonry does not effectively conduct heat to the outside of the burner.
For the most efficient heating of a space, a brick-lined-steel wood-burning stove is the best option. The bricks lining the inside of the stove absorb heat, and they slowly release that heat. For this reason, you can keep a space warm throughout the day by burning wood in a brick-lined wood-burning stove a few times a day; whereas you'd need to burn wood in a cast iron stove continuously, because heat is lost quickly through radiation.
Cast iron wood-burning stoves have a tough, long-lasting exterior, but the metal can still become damaged. Chips or pitting is most likely to occur on a cast iron stove during shipping or installation. Cast iron stoves last longer than sheet metal wood-burning stoves. Adding a brick lining to steel stoves protects the steel from heat stress and increases the lifespan of the stove. The steel exterior of such wood-burning stoves is extremely durable and, if at least a quarter-inch thick, will last for decades.
Cast iron stoves come at a premium price. Enhancements such as decorative coatings on the outside or a fan to make it a convection stove will increase the cost. A brick-lined steel wood-burning stove's price will be tied to the thickness of the steel and to other optional features built into the design.