Any kind of icy surface, black ice or otherwise, or hard packed snow - studded tyres FTW. No tread can provide equal traction on ice compared to a good studded tyre. I ride Nokian W106s myself.

But if it's slippery for other reasons: mud, loose snow, leaves, whatever non icy stuff, a tyre with an aggressive tread is often a better choice. Sometimes it's difficult to tell looking from the top (and you only need that one patch of ice to go down hard), so I like to err on the safe side myself. When we begin to have freeze-thaw cycles and rain, I start riding the winter bike with studded tyres.