I haven't heard the HE-500, but I have HE-400 and HE-6. The best way I can describe the difference is "The HE-6 is significantly better than HE-400, but HE-400 isn't significantly worse than HE-6." By that I mean, when comparing the two, it's relatively obvious that the HE-6 is definitely clearer and more open. Yet the HE-400 doesn't feel like "eww I can't listen to this after the HE-6", it just sounds like a little bit of detail loss or a "veil" if you will compared to the HE-6. That shows just how good the HE-400 is, and supposedly HE-500 is even better.
The one place significant differences start to appear between the two is once you get into heavy EQ/processing/DSP. The HE-6 takes it beautifully and is infinitely modifiable without pushing anything into clipping or distortion. The HE-400 starts getting some strange peaks and mudding up if you start pushing the processing too far, revealing the "weaknesses" that some of it's great sound is based on psychoacoustics and not true linearity. Which isn't a problem unless you go to start tweaking that sound beyond subtle bumps here or there.
If you want to run the thing from a normal headphone amp the HE-500 (or 400 if you like a dark signature) is a no brainer, The benefits of HE-6 start appearing when you want to get into heavy EQ/processing, if you have a really nice speaker amp laying around unused, you wish to get into building your rig as a 2.0ch stereo rig as well (which actually IS convenient if you want one rig for headphones and speakers), or if you want to get into some of the top shelf balanced headphone amps, of which a few are well received based on reports.
It becomes less a question of which headphone and more a question of which path do you want to head down for your setup. If you're looking for a great headphone to use in a headphone capacity, HE-500 (or 400) and don't look back. If you're a recovering stereophile as well as headphile and find some satisfaction in building a stereo rig and putting your speakers on your head, HE-6 is a fun route and squeezes a bit of extra performance out of it to boot!
FWIW, compared to HE-400, even on Lyr I can tell a positive difference between HE-400 and HE-6, but it's not as resolving an amp as would truly separate the HE-6 from the HE-500 to justify the cost.
It's hard to go wrong with the whole HE-series, really.