Between those 2 boards:
Gigabyte has 2 more SATA III ports (4 vs. 2)
Asus has slightly higher max memory speeds (22200 vs. 2133)
Asus has support for Tri and Quad SLI/CF (Quad SLI/CF vs. SLI/CF)
Asus has slightly better on board audio
Asus has Intel LAN vs. Realtek LAN
Asus is the better of those 2 boards overall unless you need more than 2 SATA III ports.
As for Asus vs. Gigabyte in general, both are good and some swear by one or the other.
So asus would be the board to go with in this comparison, also is there another mobo that is z68 that you could recommend for around the same price range? I only selected these boards, because microcenter is giving $60 off