You can't just derive the amount of current a headphone needs just by their load resistance/impedance. Sensitivity plays a bigger role than impedance alone which will determine how much power is required to drive a phone at a given SPL.
Higher impedance load requires less current and more voltage. The opposite is true for low impedance phone, current becomes important than voltage. Either way you should check the sensitivity of the headphone first . HE-560 at 90dB/mW is considered low sensitivity. I bet your vintage HP is just more sensitive than HE-560 that is why it is louder.
AKG 340 Hybrid - Sensitivity: 94 dB / mW
Hifiman HE-560 - Sensitivity: 90 dB /mW
Good point! V=IR