I think it depends on what you mean by better. If better is for use as a cable modem, the ASUS won't do anything. If better is taking up less space, the Arris is better. If better is faster wifi or wired network speeds, the Arris is better.
In almost every speed comparison, that Arris should smoke that Asus.
A separate unit like the Asus will likely offer more configuration options, and I would prefer a separate components, I run a separate cable modem, router, wireless access point. However, I don't think Arris (Motorola Mobility) is a bad brand at all, I wouldn't hesitate to use an Arris/Motorola cable modem.
Cable company just dropped off a new D3.1 Cable Modem (Arris) with 2 & 5 GHz wi-fi and it runs really well. Took a bit to get it configured, but once it was - it's very nice