Upload & Sell: On
I've used a 580EX with my 6D for the past 6 months and it works fine, but as mentioned the advanced flash controls in the 6D menus don't support the older units. You need to use the on-flash controls to set second-curtain and high-speed sync, zoom, metering mode, etc. Not a huge impediment, but it is annoying. FEB can be set on the 6D using the Q button, though, even when using multiple flashes so that's helpful.
However, I just upgraded to a 600EX and it is world's better in every way. So much so that I just sprung for 2 more and the ST-E3 and I'm selling off all my older flash units at a significant loss. If you have the funds you can't go wrong upgrading, but the 580EX is very workable on the 6D so you could take your time.