A properly used wood stove burning good seasoned firewood shouldn't smoke that much except when getting the fire going.
Once my wood stove is burning good and hot I don't see any smoke coming out of my chimney.
Wood is also a renewable source of heating fuel so Wood heat is better for the environment than natural gas or other heating fuels.
I mostly burn downed trees that were taken down in storms so they would be taken to the dump and burned there anyway wasting all that heat.