The focusing screens will NOT fit across.
The cable release will.
The 580 is a bit stronger, but mainly it's "newer" - to me, the biggest plus is that it recycles much faster, and has longer battery life (I have both). There are a number of other small differences but I don't remember them anymore, as I consider them irrelevant.
One annoying thing about the 580 is the shape of the head - it's not a nice rectangular block but rather bulbous. This makes it virtually impossible to attach a Better Beamer to it, or even a slap-on diffuser. I have one of these big "bowl" diffusers (forgot brand, was a gift) and it is a huge pain to stick on it, and then it wobbles around. I have no idea what they were thinking when they designed the head.