On the down side, having mechanical feed systems and forced air blowers, they are dependent on electricity to function, and they are noisy. They require the purchase of a manufactured fuel, which may not be available where you live. Pellets are more expensive than firewood. And, last but not least, watching the glow as the pellets are fed into the firebox can't compare with watching the fire in one of our woodstoves. We have the same reservations about corn stoves, which are economic but rely on electricity, expensive fuel, and lack ambiance.
Gas stoves are another attempt to provide the woodstove experience with greater convenience.
And, if you live in a big city where you just can't get wood, they may be a satisfactory substitute. But, they aren't woodstoves. You are still burning a fossil fuel and contributing to the buildup of greenhouse gases in the atmosphere. You are still dependent on a big utility for your fuel. And, you are not going to get the same savings on your fuel bill.