@matrix @sjw I had a hard time finding a better source on this, since propane comes in a liquid form while natural gas is... a gas. As such, propane tends to be measured in gallons/ Liters, while Natural Gas (Methane) is measured in cubic feet/meters at STP.
Anyway, it's claimed that Propane burns half the fuel in the same time as Methane. When I look at temperatures of Propane vs Methane flames, they both burn at the same temperature (around 3500°F). They also have the same ignition temperature (400°F). So so long as the stove gets an appropriate amount of fuel, Methane and Propane will probably get things hotter quicker than electric stoves, which reaches around 932°F to 1112°F.
Another way of looking at it, the energy densities between Natural Gas (Methane) and Propane are not the same. A value that I see again and again is that Natural Gas has about 1000 Btu/ft³, while Propane is 2500 Btu/ft³. Hence 2.5 times the energy.
What effect this has exactly somewhat confuses me. Obviously it means Propane releases more energy for the same amount of fuel. So a gas stove running on Methane might need to be on a higher setting to increase the amount of that reaches the burner so it releases the same amount of energy as Propane. Possibly this means that at a given setting, say at HI, Methane releases more energy than Propane and so will be hotter. But it could also be complicated if the stove knows to modulate the flow rate of different fuels. Since houses and gas stoves can be attached to both propane and Methane lines, it's possibly that this is already taken into account somehow. Then, even though Propane is obviously more efficient, both stoves can still release the same amount of energy at a given setting, and so electric stoves would still lose.
I use the small ones. Quick Boil pad? yeah that's a lie. I tried to use it at first actually, but it couldn't bring my small .9L pot to boil after 5 minutes when set to Medium (in fact it seemed to have stalled). At HI it still took it 3 minutes to go from 105°F to full boil, which was the same as the smaller pads at HI. Maybe it's intended for larger pots, but the manual for the range doesn't actually say what's so special about it when compared to the others, beyond the "3,000W element".
Doing a cold starting the electric stove might be an issue, but then it really complicate the entire problem of what's a fair test between systems. But looking at the graph, I also see that the slopes of the electric stoves are lower than for the gas. Even if I had a starting line of 100°F, electric would still lose to the Propane stove at Medium, and at HI electric ties with Propane when set at medium.