Inherently gas furnaces pipe their fumes out outside, so air quality should be better for the furnace than the gas stove, even though the furnace uses way more gas.
Exterior though, obviously the furnace is worse since its all going outside.
Good points. I wonder how the leakage from the relatively large amount of furnace gas compares to the leakage from the relatively small amount of stove gas. For example, if the furnace uses 10x cubic feet of gas and leaks 50% less per cubic foot than the stove, the furnace will leak 5x more cubic feet than the stove. (Completely made up numbers.)
Then the next question is, how does the furnace leak in the basement affect the air quality where people typically breathe?
In the summer my gas bill was $30. In the winter my gas bill would go up to about $200. One extremely cold January in 2015 nearly cost $300.
So, yeah, space heating uses much more gas than cooking.