Head-to-head feature comparison: here
Yes, they both have integrated video and audio, and both support the same CPUs.
But why is the Asus more?
1) It is GEN3, which means PCIe 3.0 slots, which have 2x the bandwidth of PCIe 2.0 slots when an Ivy Bridge CPU is installed.
2) It has a slightly newer audio chipset, how much difference this makes is unclear.
3) It has a slightly faster LAN chipset, Realtek vs Intel, though most users probably won't notice it in real-world performance.
4) It has Bluetooth on the board, which is cool if you want an easy way to sync your phone and computer.
5) The Gigabyte is Micro ATX, which while not guaranteed, usually means a smaller price-tag.
Those are just the things I can see from the comparison, there may be others such as overclocking features, etc...