Looking at the numbers here: http://en.wikipedia.org/wiki/History_of_video_game_consoles_... it looks to me like Xbox has been successful and competes well with the PS3 in North America, but has dismal acceptance in Japan. But both of them are trailing behind the Wii.

So that's clearly a success compared to the Windows-on-phones idea, but I don't think it counts as having "crushed the competition".

Xbox has been the highest selling console for six straight months now. Expect that to continue given how wildly popular Kinect has been over the holiday season.