Do you know if your cable is DVI-D, DVI-I or DVI-A? Basically it seems to me that you need the dual link DVI cable to get over 1920x1200 (which is a DVI-D).
Although if that's the case then it doesn't make sense that the same cable works on the 5850.
According to http://www.asus.com/Graphics_Cards/AMD_Series/EAH6950_DCII2DI4S2GD5/#specifications
DVI Output : Yes x 1 (DVI-I),Yes x 1 (DVI-D)
HDMI Output : Yes x 1 (via DVI to HDMI adaptor x 1 )
Display Port : Yes x 4 (Regular DP)
HDCP Support : Yes
So you need to use the DVI-D output for sure. Check the manual if you're not sure.