Gasoline has about 33 kWh/kg (118.8 MJ/kg):

https://en.wikipedia.org/wiki/Gasoline_gallon_equivalent

Unfortunately, internal combustion engines have a pathetic fuel economy since they run at low temperatures (around the boiling point of water). All heat engines are limited by the Carnot efficiency, which improves with higher temperature differential. In practice, other cycles like Otto, Diesel, Rankine and Brayton are lower than Carnot and improve with things like higher compression ratio:

Carnot efficiency = (T.hot - T.cold)/T.hot
where T is in Kelvin

https://en.wikipedia.org/wiki/Thermal_efficiency#Carnot_effi...

A low compression, naturally aspirated engine running at room temperature with nothing done to improve fuel economy runs at (373.15 - 298)/373.15 = 20% efficiency. I've heard figures as low as 8% for rubber meets the road efficiency in older passenger cars, which I believe, since we drove a ’68 Cadillac that got 5 mpg back in the 90s when gas was under $1 per gallon.

The best modern high compression engines typically achieve 25-30% efficiency at best. So I figure there are about 8-10 kWh/kg (28.8-36 MJ/kg) available in gasoline with modern vehicles. Cars built before ‘70s efficiency standards would be more like 2.5-3 kWh/kg (9-10.8 MJ/kg).

Unfortunately, it's not just that people don't care how ridiculously inefficient their vehicles are, it's that politicians corrupted by the fossil fuel industry and vehicle manufacturing lobbies never stop conspiring to lower efficiency standards:

https://www.vox.com/2019/4/6/18295544/epa-california-fuel-ec...

But I digress.

Electric motors typically run at about 95% efficiency, so we can probably assume 90% efficiency to the road. That’s over 10 times more efficient than classic cars!

Looks like Tesla lithium ion batteries are 0.254 kWh/kg (0.914 MJ/kg):

http://theconversation.com/teslas-batteries-have-reached-the...

Which is very close to the theoretical ideal for lithium ion of 0.294 kWh/kg (1.058 MJ/kg):

https://en.wikipedia.org/wiki/Energy_density#Tables_of_energ...

I'm having trouble finding energy densities for the new lithium sulfur batteries:

https://advances.sciencemag.org/content/6/1/eaay2757

https://advances.sciencemag.org/content/advances/6/1/eaay275...

I'm going to use their low number of 1200 mAh/kg, working between 1.7 and 2.5 V, so averaging 2.1 V (which is very inaccurate without integration), we can call it about 2.520 kWh/kg (9.072 MJ/kg). That would be about 10 times denser than Tesla batteries. Maybe they are estimating half the density in the real world due to packaging or something, in order to arrive at their "5 times longer battery life" headline.

So anyway, the real numbers are:

Gasoline 33 kWh/kg 118.8 MJ/kg (ideal)
Gasoline 8-10 kWh/kg 28.8-36 MJ/kg (actual for modern vehicle)
Gasoline 2.5-3 kWh/kg 9-10.8 MJ/kg (actual for pre-70s vehicle
Lithium sulfur 2.520 kWh/kg 9.072 MJ/kg (ideal)
Lithium sulfur 1.260 kWh/kg 4.536 MJ/kg (actual)
Lithium ion 0.294 kWh/kg 1.058 MJ/kg (ideal)
Lithium ion 0.254 kWh/kg 0.914 MJ/kg (actual for Tesla)

My numbers might be off by a fair amount, but the important thing here is to think in orders of magnitude. Lithium sulfur is halfway to the energy density of classic cars and aircraft, with all the positives, like electric motors having 10 times the power as gas engines by weight, much higher torque, and substantially higher endurance/simplicity.