"Double the size of the battery and you double the power of the car"
Double the power *capacity*. There's a limit to how much current the motor and cabling can pull before the magic smoke escapes.
"So the quickest 0-60 time will always be the from the car with the biggest battery"
Not necessarily. That's true if the power delivery capacity of the battery is the limiting factor. The lower capacity but lighter car may accelerate faster if the motor or tyre traction is the limit.
"Same is true for charging - the bigger the battery, the higher the power you can pump into it to charge"
Probably not. You can't push current into a battery faster than the charger or cabling can cope with, so the bigger battery at the max current of the charger will take longer to charge from empty than a smaller one.
"electric car once you're up to 60mph you can use regenerative braking to recover about 50% of the energy back into the battery"
Only if you're slowing down, regen braking uses the car's momentum to use the motor as a generator. A petrol engine's management system will turn the fuel off when coasting, effectively the same thing. Once stopped (unless you have auto-start-stop on the engine) it will use some fuel idling the engine where the electric uses none.