I'm not a fanboi or hater of either technology and I have no issue with buying one of each, or recommending either one.
The biggest differences are (1) Roku supports Amazon Prime, (2) Apple TV supports iTunes, (3) Apple supports Air Play from an iDevice. If you are in the iTunes ecosystem you probably should get an Apple TV. If you are not a big iTunes user and you are an Amazon Prime member, you probably should get a Roku. If you have lots of iTunes content and are also an Amazon Prime member, maybe get both or hook up a PC to your HDTV.
I am cutting the cord. I got the Roku 3 for the livingroom TV because it gives us the most content options; I might get a Apple TV for the kid's room because my daughter has an iPad. With the money I am saving every month by dumping cable, the cost of an Apple TV or a Roku 3 is minor.
Apple TV's user interface (what you see on the screen and how you navigate through the content) is infinitely better and easier to use than the Roku 3. Whatever service or App you are using in Apple TV is simply laid out and that same layout follows through to all the different apps on Apple TV. This goes for version 2 and 3. When it comes to Roku 3 each app (or channel) looks different. So you're constantly having to remember how to navigate through the many different channels that you might want to use at any given time. The reason for this is Apple requires all its providers to use their template so that navigation looks the same from app to app - this way you have one type of user interface to navigate through. Roku 3 allows the provider to design their own use interface, so on Roku 3 Netflix will look different than Vevo, which looks different than Amazon, which looks different from ... and so on. Also... setting up those premium apps (like Netflix, Hulu Plus, etc) are easier to do on the Apple 3 (and the 2 - since they use the same basic ios). You never have to leave your TV in order to sign up, or sign into these premium apps. Roku 3 (and all previous versions) requires you to stare at a code on the screen, go to your computer, and log into their website in order to pair the service to your Roku with the code. That. Is. A. Hassle. You COULD do this from your iPad if you have one, but most of the Roku sites are not optimzed for ios. and if you have an iPad... you'd get more use out of the AppleTV in the long run since it allows for Mirroring to the apple TV box.
In short? I personally feel there is NO comparison to Roku. The Apple TV experience is much better by leaps and bounds.