Both hardwood and softwood are great for burning on fires and in log stoves. Because of their density hardwoods will burn for significantly longer on an open fire than softwood. In a log burning stove the advantage of hardwood over softwood is less noticeable.
Softwoods are considered more sustainable than hardwoods, because they grow faster and are more readily available.
Avoid burning any waste woods, such as old pallets, as their may be noxious gases and residues produced.