I am not sure why these devices are discussed in the Google TV section. I don't own an Android mini PC or mini stick or Android TV, not sure what they are supposed to be called, but I do own Roku and Google TV. As far as comparison to Roku, I know there isn't much other than both can stream internet TV content and that obviously means a lot of the same content. Roku is so easy to set up and the channels make accessing the content very easy and Roku despite using a very modest processor is optimized for streaming and provides really good quality for the most part. Much of the content accessible by Roku will be accessible with an Android mini PC web browser but Roku will probably be a much better option for content both can access. It is also likely the Android mini PC can access a lot of content not accessible with Roku since Roku doesn't have a web browser, all content is accessed by Roku channels set up by Roku or third parties providing private or public channels. Google TV does have a web browser and I can access a lot I can't access with Roku as a result, but for the things both Roku and Google TV do, Roku usually does better or easier so I use both.
If you are a cord cutter and just want to have an easy way to access content and Roku provides the content you want, it is probably the best option. I don't know how these little Android boxes would suit someone looking for an easy way to watch TV after returning their cable box, I suspect not very well. Google TV differs by being designed primarily to work in conjunction with a traditional TV source, I use OTA and Google TV combines internet TV sources with an OTA guide and the modified Google TV Android operating system is much friendlier for this purpose to my way of thinking than standard Android. Google TV controls my TiVo and everything is viewed using the same control and same HDMI input on the display, the female head of household sure finds that preferable to any other setup I have come up with. My only other Android device is an HP TouchPad running the cyanogen mod Android 4.0x so I am far from an Android expert.