In the early 1820s, the first propane stove were invented. They were patented a few years later by James Sharp, who also opened a factory to make them.
It was not until the 1880s though, when the gas stove finally took off as a commercial item. Later in the 1930s, the electric stove became popular, and began replacing many gas stoves.
The benefit of a propane stove is that the temperature is ready in an instant, where as with electric stoves the heat gradually comes into the coil, and eventually leaves the coil. There is nothing instantaneous about the electric heating process.
The benefit to electric stoves are the flat tops which can evenly distribute the heat.
Both the electric and the propane stoves are very durable if they have the metal coils. The glass-top electric stoves, though, are not as durable.
They have weight limits because they can break under too much pressure. The glass-top electric stove can also break when something has been dropped on them.
Propane stoves can be ready and heated as soon as you need them. They also are great during storms if you lose your electric because they do not need electric, just a sufficient amount of propane.
Keeping up with the propane and making sure it is full can be a pain, where electric is generally readily available.
Propane stoves are a little more expensive than electric stoves to buy. When paying bills, those who cook a lot save approximately $20 a year using propane, and those who cook less tend to save money with an electric stove.
One major issue: Many times you have to pay for propane in bulk a few times a year, which can be a blow to the wallet.