Looks to be an issue of impedance. The AKGs are rated at 55 ohms and the Sonys at 24. So I think my solution is to replace the Sonys with another pair of AKGs.
I have a pair of AKG K141 headphones. I also have a pair of Sony MDR V4s. When I connect both sets to an A/V receiver using a 1/4" splitter jack, the AKGs suffer a considerable loss of volume while the Sonys do not. I believe the AKGs are analog and the Sonys are digital; both pairs are pretty old but in good shape.
Right now we can't use the splitter without the Sonys being too loud for comfort in order to have the AKGs loud enough to hear.