ChromeCast only supports a handful of apps like Pandora, Netflix, Youtube and Hulu Plus. There's no interface like the Apple TV. It's just there waiting on you to begin streaming. You have to configure and manipulate it using your mobile device.
Handing off the streaming URL directly to the Chromecast is awesome though. It frees up your mobile device. Apple needs to expand their support for their AirPlay version of that feature. Currently, device less streaming only works with iCloud purchases.
Chromecast can't do mirroring either and the Chrome browser plugin is in beta (it's a little janky).