My board has both.options as well.
@ better -- what do you consider to be better? Both connect your computer to the router and both K this just fine.
The difference is options. With the Killer you can prioritize certain applications in their allocation of bandwidth. The Intel chip has some features which are good if you're part of a (home)network or need remote access.
I personally use the Killer chip on my board.
In terms of being connected to the internet I cannot see any difference. It does the same job as the Realtek Ethernet chip on my old board.