Now maybe my gear isn't expensive enough to tease out the differences in the low and mid-low frequencies between theses headphones, but I do have 3 amps: the fiio e9, the Little Dot MkIII, and a vintage Kenwood receiver, and none of these amp choices can change the he-400's or he-500's low-end and low midrange reproduction, especially with male vocalist.
I don't know if cost is important but power is, especially for the HE-500. Now that the Gugni is out, powerfull and cheap seem to be possible nowadays.
I don't know about the Kenwood but the Little Dot is too weak for the HE-500. The Fiio has more than adequate power but its output impedance might not be adequate for the low impedance orthos.