The Watt-hours per kilogram of good Lithium Ion batteries is around 250-280 Wh/Kg; for Lithium Iron Phosphate it's about 180 Wh/kg, and for Sodium-Ion about 170 Wh/Kg.
The raw energy in gasoline is about 12,300 Wh/Kg but automobile internal combustion engines get only about 20-30% efficiency yielding about 2500-3600 Wh/Kg. For aviation piston engines it is a bit better at 25-30$ so 3000-3600 Wh/kg.
So, the batteries, instead of being 10-12X the weight of the gasoline for the same net driving/flying range, could weigh about the same as the gasoline. So, a typical car with maybe a 16 gallon tank and 30 miles per gallon fills up with 128 pounds (58 kg) of gasoline to get 480 miles of range. The Li-Ion battery for that range would weigh something like 1300 Lbs (590 kg). That is a substantial additional weight for a car that could be 2800-3800 Lbs in ICE configuration, so 35-45% added weight (a bit less because of savings on the ICE engine, etc). This requires everything else to also be heavier, from the structural frame, the suspension system, and even the wheels and tires (which is also unsprung weight, further impairing performance).
With a 130Lb/60kg battery instead, and saving the weight of the ICE engine and fuel system, the overall car design could go much more lightweight, regaining a lot of performance and range, all while gaining the huge torque of electric motors.
In aviation, a battery systems of that weight would enable all-electric aviation to go from small performance niches to the default for general aviation.
So yes, it would be a HUGE benefit to achieve 10X energy density batteries, and we do have reference points for people to imagine it.