The only thing the Roku Box has over the Apple TV is the ability to play Amazon Prime Instant Videos.

Other than that, an Apple TV with an iOS device can use AirPlay to stream just about anything. Take a look at this list for example. The one app missing from that list is one of my personal favorites, Plex. It also works via AirPlay to the AppleTV. Technically Roku is more open than the Apple TV. But as long as you have an iOS device, your options are far, far broader.