I'd get the 770. Nvidia drivers are more trustworthy. AMD drivers always seem to introduce odd quirks such as wake from sleep issues, HDMI audio issues, runt/dropped frame issues, etc...
Ever since I switched to Nvidia cards, I haven't had any driver issues. The 770 is a solid card and if you can get your hands on an OC or SC edition, you'll get performance matching or close to a 780 for $150 less.