With Microsoft? They would've made some cult classic games that sold poorly but were loved by those that played them, then would've ended up getting shut down.

With Sony? 50/50 between being a big success and remaining as a strong 1st party dev or making some decent games for awhile but then ending up as a casualty of Sony's shift to focus on the western market instead.

The Microsoft scenario is unrealistic. They simply were not a fit for Xbox at that time. Probably wouldn't really fit right now either, though Microsoft is branching out some now, so maybe it could work today.

Sony could have gobbled them up. My guess is things would be pretty similar. Their games would work fine on PlayStation.

In neither case would it have ended well. Microsoft's handling of the Japanese market and Japanese development community has ranged from poor to disastrous, and Monolithsoft would be no exception.

That said, Sony doesn't have the best track record with in-house Japanese RPGs, either. They've made a few attempts at the genre, but other than Wild ARMs, none of them spawned long-running series. Even Wild Arms died with the PS2 and PSP. And they pretty much shuttered their Japanese development years ago,

Only Nintendo would have given them the time and resources they needed to shine. Nintendo wasn't perfect in their handling of Monolithsoft either, with Nintendo of America's mishandling of the original Xenoblade on Wii - thanks a lot, Reggie :P - but Monolithsoft filled a niche Nintendo wanted and needed.

That would almost certainly not happen, as Monolithsoft was created to make Xeno titles. It’s not likely Tetsuya Takahashi would give up the core purpose of his studio. The main reason they broke-up with Square, and then later with Namco was because those companies were insufficient.

I doubt that with either Sony or Microsoft Monolith and Xenoblade would have become one of their greatest and most valuable assets as they are now with Nintendo. Sony would have dumped them down after Xenoblade would have sold a few hundred thousand copies on the PS3 and Microsoft wouldn't have even bothered to let them do their thing in the first place.

It's tough to say. If somehow Monolith went to Microsoft, I don't see it as enough to change the fortunes of the Xbox in Japan by much at all. Look at all the Japanese titles for the Xbox 360, which still couldn't sell 2 million in Japan.
Sony might've worked out, and I know we'd get better graphics in Xenoblade if it was on PlayStation.

PRetty much what is being said here. At best they'd be a rather niche end of the Sony or Microsoft strategy, but would most likely not exist at all, and certainly not create the successes they have since Xenoblade 1`.

Given Sony's history published or new IP RPGs. Xenoblade likely dies after the first entry.

Sea of Thieves under MS Rare is their most successful and popular IP.

Yep. If Days Gone didn't survive, Xenoblade is as doomed as Star Fox Zero.