There's a big difference in the BTU's per cubic foot between natural gas and propane. I couldn't find which burns hotter, just which has more energy per unit volume.
First, Natural gas is a mixture of hydrocarbon gasses, but is about 3/4's methane which is the lightest hydrocarbon with only one carbon atom per molecule. Propane is a purified hydrocarbon with three carbon atoms per molecule. There is some propane in matural gas, but basically you can consider it to be methane.
Natural gas varies a fair amount depending where it comes from and also the temperature when it was extracted. Propane is pretty much the same everywhere. LP gas is mostly propane and can be considered the same for most purposes.
Now the figures: Natural as has around 1000 - 1100 BTU's per cubic foot while propane (gaseous) has about 2500 BTU's per cubic foot.
To switch between fuels, the metering jet or nozzle has to be changed. You can't use these two fuels interchangeably. Almost any gas burner can be modified to handle either and you can often buy a kit from the manufacturer to make the change. The heat output of a burner is a factor of the fuel itself and the volume of gas delivered, so Mike's smaller LP burner is probably delivering quite a bit lower volume of gas than his natural gas range.
Natural gas is for the most part, pumped out of the ground and cleaned up a little before it heads out in a pipeline. Propane is purified from natural gas or from refined oil, then stored and shipped in containers. For this reason, even though propane has more BTU's per volume, oit is costlier to manufacture and is therefore more expensive per BTU than natural gas.
Probably more information than you needed, but I looked it all up so I thought I'd share.
