Car battery (lead acid) discharges much, much faster than it charges?
You are entirely correct. The issue comes down to the fact that it's pretty easy to overcharge a lead-acid, but normally you try not to "over-discharge". So you have to be careful about the last stages of charging. This is not (exactly) true for discharging, but that is only true because you don't want to completely discharge lead-acid anyways. Unless you have a deep-cycle battery, you don't want to pull more than about 50% of the available charge out when discharging. If you do, you'll severely reduce the battery life.