So 'better' depends on the components you are putting in your computer....
The gigabyte board would be better if you plan on doing crossfire or sli. It has 2 pcie 3.0 ports which run at x16 and x8 vs the ASUS board which runs at x16 for one pcie 3.0 port and x4 if you crossfire or sli.
I also notice that the asus board has one more SATA III 6gb/s port than the gigabyte board does. If you plan on having more than 2 SATA III enabled devices in your computer build then you might wanna consider the ASUS board.
The Asus board is cheaper on newegg.
Asus, in my experience, has great customer service. Gigabyte, however, I can't speak for. Someone else on the forum might be able to better help you out with that but from what I've heard, people give mixed reviews.
The gigabyte board has 2 more usb 3.0 ports if you have a lot of usb 3.0 peripherals for some reason.
The reviews are pretty good for either board. Honestly, if you're not planning on crossfire or sli just go with ASUS. You won't notice any kind of performance difference between the two.