Nintendo owns Japan market which is the biggest for portable market, Sony owns Europe and XBox has been strongest in USA. Trying to win Nintendo in Japan is a tall order, so I dont think Sony would go there.
MS practically only has a foot in the USA. They are "relevant" in EU and non existent in Japan. PS4 owns both USA and EU right now. I suspect that the Switch will pass the X1 in the US lifetime sales as well, and yes Nintendo owns Japan.
While they still have a strong presence in the US, they are losing ground fast. X1 has been behind the PS4 from the start, even in the US. The 360 just landed in the right place at the right time.