As Nikola Tesla and George Westinghouse proved, it is far easier and safer (and therefore less expensive) to conduct high voltage current over AC than DC. That being the case, it is less expensive and easier to provide high capacity L2 charging than L3 DC charging so most places are going L2. Probably the reason there are so many more L2 stations out there.
AC and DC "conduct" equally well, it's just that AC is extremely easy to bump up or down, by simply running it through a transformer. You can distribute AC over long distances at very high voltage (to minimize resistive losses in the wires), then bump it down easily at its destination. Multiple taps on the transformer allow easy tweaking to get the actual voltage close to the nominal 110, 208, 240, 480 or whatever is needed. DC is far harder and more expensive to level-shift.
L2 and L3 charging both require a "charger" to convert the AC line voltage to the proper DC voltage and current for the battery on the vehicle. The only difference is the location of the charger. L2 chargers simply bring the AC line voltage to the vehicle, which has its own charger, tailor made for the vehicle's battery. L3 puts the charger on the ground, so each vehicle doesn't have to carry its own charger, which is nice because chargers are bulky, heavy and can run hot. You can also make the charger monster-sized (since you only need one to service all vehicles), so it can charge vehicles with giant batteries fast. To service all the batteries that are out there, some sort of signaling protocol is necessary to tell the ground-based charger how much current to supply, at what voltage.