Before the 650s were out, I had the 580s and 600s, preferred the 600s.
When the 650s came out, I tried the 650s and stuck with them for a while.
I sold and repurchased the 650s twice. (Can you hear my wallet screaming?)
But now, I'm back to the 580s.
What can comment from my journey:
1. The 650s may be more "hi-fi" in that the sound is more refined and less edgy. Everything sounds just so well rounded off, there's very little harshness. With a capable amp and good amount of volume, the 650s can really come alive. At lower volumes, the cans sound veiled and distant. Build quality is top notch, I personally prefer the 600/650 build and looks over any other dynamic headphone on the market, period.
2. The 580s have a more immediately likeable frequency response, but it sounds slightly harsher and unrefined. It sounds more exciting, and you can enjoy the 580s at lower volumes than the 650. The build is excellent but the paint has a reputation to chip/rub off easily over time. The 580s feel nicer on the head because it's lighter.
Why did I switch from the 650s to 580s? Well, I was starting to get bored with its sound signature, and I wanted the extra $200 in my pocket. Maybe in a few months I'll switch back (or have both).
Conclusion - if your HD650s sound muddy at volume levels you're comfortable with, you should most definately try the 580s. If you really like the 580s then you can invest a bit more and get the 600s. If not, oh well, they were a fraction of the price of the original HD650s anyway.