AC can allow for thinner gauge wiring, which is lighter and costs less. This is mostly because AC is typically a much higher voltage as compared to DC. In GA aircraft, the currents involved don't justify the added weight and complexity of transformers and separate electrical buses. Larger aircraft - it can shave off enough weight to be substantial. While DC could technically be more efficient at higher voltages, there are lots of practical reasons that you don't want a 400vDC electrical system: It arcs, promotes corrosion, difficult to step down, no batteries available at those voltages...
It is also much easier to get "clean" AC power without too much noise in it. DC tends to have a lot of ripple, so needs to have voltage regulators which add to the losses.