I think Switch will do pretty well, but from what I've seen of the system, it is so far removed from where the Playstation and XBox brands are that Nintendo basically is not really competing head on with those devices anymore. Nintendo can call it whatever they want but it's a mobile centric platform, 70% of their own launch video highlighted people playing the device on the road. Nintendo is effectively an all portable hardware company basically now. Right now NS will be the higher end, 3DS the lower end.
Having said that, given that Nintendo has embraced iOS/Android and is looking to expand their IP, I think a deal with one or both of Sony/MS will happen at some point to ensure Nintendo's IP have the widest reach as they look to move into the movie business and theme parks and all that.
In return I think Sony and/or MS could agree to make Switch games and also offer Nintendo sweet money-hats. So you could see Halo Switch or Uncharted Switch, it wouldn't just be a one-way street. Especially now that Sony is probably not making a Vita 2 ... there is nothing directly competetive from either Sony/MS to the Switch. If Sony was making Vita 2, that would be a natural competitor but it doesn't look like it's happening.
So it won't be "Nintendo goez third party dooood OMG!", but I can see Nintendo cutting a deal with one or both but continuing to be their own hardware maker, just on the portable console side, which neither Sony or MS compete with. And it won't be all Nintendo IP, just a few select games of Nintendo's choosing, just like are slow rolling out their IP on iOS/Android for maximum exposure.
