I will be using 3x1080p monitors at 60hz each. I need to know which of the two GPUs will perform best with this. both will have gigabyte's WINDFORCE after-market cooler attached.
For a 3 monitor setup or for any setup you should go with the ASUS R9 290 DCUII http://www.amazon.com/gp/product/B00HS84DFU. The GTX 770 is a level below the R9 290 in performance.
For your setup specifically, the R9 290 will shine even more with the extra horsepower and VRAM that will be required to push 3 1080p monitors.