Not even close, diesel/gasoline stores 35 MJ/l, a good battery (lithium-metal, much better than lithium-ion), 4.32 MJ/l
Now, if only we could extract 90% of that diesel stored energy.
An awful lot of energy consumption is just fine with waste heat, it doesn't need a heat engine. There you get 90% efficiency even with heating oil.
that said, diesel is mainly used in large trucks and shipping vessels, where I would imagine energy per unit volume would be more important than energy per unit mass. if electricity were much cheaper than diesel fuel, it could certainly become the economic choice for all but the longest routes.
[0] https://en.wikipedia.org/wiki/Diesel_engine#Major_advantages
Regenerative braking helps more for stop-and-go driving in cities but it's basically meaningless for long-haul trucking or shipping.
Meanwhile, the average passenger car in 2000 created 11,000 pounds of co2 over the course of a year... I don't think I had seen that number before - no wonder there's a problem. https://en.m.wikipedia.org/wiki/Exhaust_gas
"Grandpa, tell me again about combustion engines."
"Well, they burned gasoline in a series of tiny explosions, and they were set up so that the timing of those explosions would generate motion."
"Haha, that sounds like a Rube Goldberg machine."
"Yes, and the worst part is that fire is hot. So even though gasoline contains a lot of energy, the process of turning it into motion was fantastically inefficient. They turned so much of the energy into useless heat that they needed whole separate systems just to throw it all away so the darn things wouldn't melt."