Wood stove and coal stoves operate similarly, and neither is inherently more dangerous during normal operation. Differences in coal combustion and wood combustion, however, mean the owners need to be careful when switching from one type of stove to another.
Coal stoves produce far more ash than wood stoves. While wood ash is useful as a fertilizer, coal ash is toxic, and it presents a potential fire hazard if it's not stored properly. Burning wood produces far more particulate matter than burning coal, which can cause material to build on the inside of the chimney. Wood stoves can also produce hot material that can escape through the chimney and start a fire.