The ASUS card has better and custom components as well as their famous Digital VRM. This means the card gets much better power delivery. The Gigabyte Windoforce is known for its amazing 3 fan cooler, so it will stay cooler.
Both cards have excellent cooling, with the Gigabyte one being a little better, but louder at stock.
As for PCB, the Gigabyte's is a reference GTX 680 PCB, but with no "real" custom parts that would assist overclocking, unlike the ASUS card.
The bottom line is, if you want to overclock your card as high as possible on air cooling, the ASUS card is the way to go (although the GTX 670 design allows for quite a bit of overvolting, so the Gigabyte Windforce could compete here as well), but as for cool cards, the Gigabyte's card would be your best bet if you do not want to overclock very high.
If you do plan to go with water-cooling at all, ever, the Gigabyte Windforce card would be better due to its GTX 680 PCB that have an abbundance of waterblocks available.