I read a review of the 501's and it said the bass response was better on the 580's. I only have Best Buy and Circuit, so I can't try out anything good.
I've not done a direct, side-by-side comparison, but have listened to both. I'd say the bass response comment is basically true. But I think it makes for smoother, more transparent reproduction overall. While
slightly less detailed, I find the AKGs more transparent, with better soundstaging/imaging - very smooth, open, and airy, if you like that kinda sound. Keep in mind, though, that I'm not a bass hound. IME trying to squeeze monster bass out of the tiny little drivers in headphones = something else is going to sound screwy as a result.
I think the 501s really need a good amp to drive them. I'm in limbo right now, with no DAC/amp for my 501s, and though I have grand plans to pick up a tube amp for my K501s to warm them up just a touch and add a bit of low end oomph, unfortunately it's not a priority at the moment. I suspect you'll be happy with any of the three listed - they're all quality headphones. Maybe poke around over for reviews and feedback at headfi.org if you haven't already.