Natural gas is methane CH4. When it burns, it combines with oxygen gas O2 to form 1 part Carbon dioxide (CO2) and 2 parts water vapor H2O. Because the water is released as water vapor, you lose the heat of evaporation.
Propane is C3H8. Thus, when burned, it forms 3 parts carbon dioxide and 4 parts water vapor. Because the ratio of carbon dioxide in 3:4 for propane compared to 1:2 for natural gas, propane is a more efficient fuel. However, is you are concerned about release of CO2, both have an issue.
Although seldom used as a cooking or heating fuel, butane as often used in fire lighters, is C4H10. Thus, when burned, it forms 4 parts CO2 and 5 parts H2O. Thus, it is an even more efficient fuel than propane.
It is the variation in fuel efficiency of the various hydrocarbon gases that the nozzles have to be a different size. While you could burn natural gas in a burner designed for propane, fewer BTUs would be released. By using a slightly larger orifice for natural gas, you can restore the heat output.