In a side-by-side comparison of the two units I sadly found the AppleTV to just be frustrating, while the Roku is a pleasure.
For instance, consider the Netflix apps available for each unit. The Apple is a maze of menus, frequently forcing me to back-out or dive in a few levels. Roku more intuitively lets me get to the content I want without nearly as much menu-ing around. Almost across the board Roku makes it easier to get at the content I want, the only exception being content stored in iCloud.
To get my Apple content to play via Roku I use Plex, it is quite easy but not as integrated as Apple-to-Apple. I can, however, use Plex to stream almost any content that is on my Mac to the TV. Conversely, to play non-Apple content on the AppleTv is a pain. Amazon Instant Video, which is a primary source of media for me, is a terrible kludge using Apple's AirPlay to relay streaming content to your AppleTV. It works but only when I have a really reliable connection. Roku's native Amazon app just works.
The amount of media available to explore on Roku seems pretty endless. The device itself feels faster and snappier than my AppleTv. It is very rare that I've found Apple to be so far behind but Roku won me over!