I don't see them being competetive in the UK, and I think they will be beat fairly soundly in the US too. 

Now that Sony has made the PS4 the "go to" platform games like COD and Star Wars Battlefront and Batman Arkham series ... MS basically has Halo and Gears and to be honest both of those IP are getting a little tired. 

It would be the best for the industry. Last Gen had fierce competition and is by far the best one for gamers. MS in charge of hardware+infrastructure and Nintendo in charge of the gaming divisions would create a powerful combo.

I don't think a Sony-Nintendo partnership would work even though they are closer in terms of being Japanese companies.

The reason why is Sony needs every penny they make from the game industry.

Microsoft ... lets be honest, even in a good year for the XBox, the money they make from games is just gravy to them. Doing well in the game business is more of a feather in the cap for them. 

They likely would be more willing to simply let Nintendo have the bulk of licensing fee profits and things of that nature, provided Nintendo would be willing to do things like incorporate Windows 10 (especially on handhelds) and maybe throw them a bone with things like some Hololens support and things of that nature.