I'd expect MS to have more powerful hardware this time but I doubt it will have anything to do with Nvidia because 1) One X would provide really good experience for pushing the engineering in a consumer device which will help a lot. 2) MS hasn't put as much into first party titles as Sony so there's a stronger need to provide third party experience that's best as well as online services which are more refined. 3) MS has more money and can afford push more in this regard. 4) MS vision: BC, online services, development tools are somewhat ready now. MS can simply wait for hardware that is viable and release next console and fill in any software gaps with BC till third party or first party offerings are ready.The only justification for Microsoft going with NVIDIA the next generation would be to leapfrog Sony on the GPU front. As NVIDIA has better performance per watt and better performance per mm, as well the faster architectures on PC. But that doesn't necessarily translate to a better custom GPU design for consoles. It might not matter at all.
Sony will likely be comfortable releasing a machine that is strong graphically but relying more on first party to drive interest. Further I think Sony is going to have a real issue if PS5 is not BC, I think some of their budget is going to have to go towards developing that capability. And I'm not sure Sony has tools as far along as MS which would potentially eat even more into a budget. And keep in mind Sony will have multiple teams working in first party which will also compete for cash.
In any case I don't think MS needs to anything radical like partner with Nvidia to gain a hardware advantage. They can simply build a larger APU and devote dollars to keeping it cool and quiet.