DC at low voltages (1500 and below) tends to be used for older systems becuase it's technically simpler. DC supply, DC traction motors, no need for transformers or rectifiers on the vehicles. The downside is you need more complexs lineside equipment to convert the high voltage AC grid power to low voltage DC. Also, the lower the voltage the higher the current - so you need much heavier OLE and the volts drop with distance is far highre so you need power feeds to the OLE every few miles.
Main lines these days are high voltage (25Kv) AC which allows much lighter OLE becuase currents are lower and simpler power collection from the grid (which is high voltage AC) and much greater distance between pwer feeds into the OLE because the lower current means less voltage drop with distance.
The disadvantages of AC traction used to be the complexity of the on-board tnasformers and rectifiers to convert the power to low voltage DC for the traction motors, which led to reliabilty problems with early AC locos on BR. These days high voltage electronic control has been developed, as have AC traction motors. Pendos, for instance, still use transformers to reduce the voltage, but instead of rectification to DC, the AC waveform is electronically modified to feed the AC motors, the frequency varying to modulate motor speed. They can also use regenerative braking, where the motors generate power and feed it back into the OLE while retarding the train. Clever stuff to do that with AC, with the required phase matching.
CS