I doubt Nintendo wants anything to do with "Xbox", it would be strictly about certain property and services..
Lets imagine what this type of deal would be like, assuming MS wanted to shift their gaming business and approach Nintendo. The biggest question, is not about OS, services or achievements, but does Nintendo have interest in diversifying its catalog (with games like Halo & Gears)? That would be the incentive for partnering with MS (not just exiting the business and letting Nintendo presumptively benefit from the void). Even though it would be advantageous for Nintendo & modernize w/ "live", achievements , better OS, etc I feel Nintendo doesn't really care much for that, and would only come as a byproduct of an agreement that nets Nintendo popular online titles (remember Ninty's charging for online soon).
Now its clear Nintendo has its eyes on that online service $$$. After many hours of Kart 8 deluxe, I can safely say its the same ole crappy online that Nintendo will soon start charging for. To gain or come close to the ultimate desired subscribers (1:1) as possible, you obviously need popular online games to justify that service charge and IMO is what Nintendo would be vying for the most under this premise.
In the end, certain MS games would become Nintendo/PC (cross-plat online) and Nintendo would make some unique, exclusive content for windows store, and run a form of Windows OS & live on their consoles. We'd see the online price hike to the standard at this point where MS rakes in a 60/40 or better deal. That's how I'd imagine it went if MS were to shift their gaming business and dealt with the big N.
