Basically the Black edition is more stable if you overclock it.
The normal 5970 is still overclockable, but you will run into more problems than you would with the black edition. It is a lot like with BE CPUs.
In my personal opinion the normal 5970 doesn't need to be overclocked. It is a beast at stock speeds.
I'm not sure but I THINK that the Black edition may come with better cooling (for example beefier heatsinks) but I could be wrong.