115V 400hz Alternating current is generally more efficient than 28V Direct Current when powering motors. The wiring for 115V current is also lighter, due to the reduced currents involved compared to a similar 28VDC device.
Example:
A 100W lamp will draw .86amps @ 115VAC while the same 100W lamp would require 3.6amps @28VDC by comparison. Higher amperage loads require heavier wires to carry the current. Most lamps can operate on DC or AC as long as the voltage is correct.
The majority of the main aircraft systems using motor-driven pumps and fans are usually AC powered. The windings and cores on an AC type motor are lighter than a DC motor with comparable output.
All DC powered items are usually there as a backup or standby unit for redundancy. There are also convenience considerations for when APU/Engine Generators/Ground Power is not available.
Many electronic units, while they may be mainly AC powered, have internal TRUs to reduce the voltage and convert AC to DC. Practically all electronic devices from transistors to integrated circuits rely on DC power (whether converted AC or direct from DC) for operation. +/- 5V, +/- 12V and 28V are all common internal operating voltages. Some units will also internally convert 28V DC into AC for operation.
There are many systems that require both DC and AC power sources to fully function and the loss of one or the other require special procedures to overcome system shortcomings.
In the days before the switching power supply was in use, an inverter (of sorts) consisted of a DC motor directly connected to an AC generator and was quite common aboard aircraft pre-1960s. The vacumn tube era comes to mind here.
Direct Current:
Electron flow is steady from negative to positive
Is the most reliable power source aboard due to the aircraft batteries
Cannot be easily up-converted
Alternating Current:
Electrons are bouncing to and fro at the output frequency
Is subject to loss with engine outs and generator/inverter failures
Can be easily and efficiently up/down converted VIA a transformer
Cheers