both the 970/980 and 1070/1080 cards will work, as long as they are not overclocked or factory overclocked (TI) versions
a overclocked video card or "TI" model can draw over 230 watts compared to the 180 watts of the factory stock models
you will need a 6 to 8 pin power splitter if using the stock 850 watt power supply which has only two 6 pin gpu cables on the z800
i currently run a GTX 970 on my z800, but i have the 1100 watt supply