Nintendo would not have allowed the game quality to slump that much if they had bought the remaining shares of Rare, you bet your ass Rare's designers would've gotten an earful from Mr. Miyamoto and the Japanese staff for any sloppy design. Almost every dev that works with Nintendo takes their game up a notch, probably because Nintendo doesn't fuck around with that stuff. 

Banjo-Threewii and Diddy Kong Racing 2 would've sold a ton the Wii and/or DS too, and likely other Rare IP too ... they missed out on the Wii/DS era where Nintendo had a huge userbase. 

No. Rare has produced many good products you simply may not have played. Grabbed by the Goulies is fun, Conker Live & Reloaded would not have happened on another Nintendo console, Perfect Dark Zero was good in it's day, the Viva Piniatas were well received, BK: N&Bs was decent, and the Kinect games were of quality. Have you ever played Kinect Sports Rivals? No? It's actually a really good game not possible on any Nintendo console.

Rare is fine with Microsoft. Sea of Thieves was well received at E3 with many gamers excited in anticipation.

Kameo Elements of Power was a fantastic game with a very original and enjoyable premise. (You turn into other characters to solve puzzles.)

Viva Pinata I had to ban myself from ever playing again due to how addictive it became, once I decided to play for an hour... Didn't realize the sun was coming up 12 hours later.

And Banjo Kazooi Nuts and Bolts, whilst it did lower the emphasis on platforming... I enjoyed it's building mechanics.

Perfect Dark: Zero didn't live up to the original (Which let's be brutally honest, it's a stupidly impossible task) and I disliked the voice acting, graphics were fairly decent at the time as well.
It was an average game, nothing ground breaking.

The Kinect games were just shovel-ware and ironically, their best selling efforts in recent memory.

Killer Instinct, whilst not entirely made by Rare, but using Rare's I.P. Was probably one of the greatest fighting games of this entire generation and is one of the bright spots for the Xbox One.

I am actually looking forward to Sea of Thieves.

So far, I have bought every Rare game on Xbox, Xbox 360 and Xbox One and I have been fairly pleased about it overall... Many of the games could have probably done better financially if Microsoft gave the games a better advertising budget.

Would Rare have been better with Nintendo? Well. That's hard to say, if Nintendo bought Rare and Rare didn't bleed employee's, then yes, they probably would have been better.
But then again, Rare might have just been tasked building games based around Nintendo's I.P rather than bringing us something new.

You say that but Nintendo has published Rare games of shoddy quality before like Mickey's Speedway USA and Conker's Pocket Tales ...

Conker Live & Reloaded wouldn't have happened but that's only because the Conker sequel would have. It is known knowledge that Chris Seavor was already in the early stages of working on the next Conker game despite the low sales of Bad Fur Day. The entire storyboard and initial planning for the game had already been completed. The reason the sequel never saw actual development was because of the Microsoft buyout. Microsoft felt that Bad Fur Day just had a run of bad luck and decided it needed another chance on Xbox. When Live and Reloaded failed to generate sales, that's when the sequel was cancelled for good. As for everything else you said, I would argue that Rare's best efforts under Microsoft was Viva Pinata.

The big question is would Rare have been better off with Nintendo? In my opinion, from a marketing perspective, yes. Nintendo knew how to sell Rare's games. Rare knew how to make games that would sell on Nintendo consoles. When Microsoft bought Rare, they looked at Rare as an equivilent of a third party developer and thought their games would sell well no matter what. The thing is, by that point, people bought Nintendo consoles for Nintendo games AND Rare games. So the people who wanted Rare's games already bought a Game or were planning to buy a GameCube. Also, Microsoft had no idea how to market these games. They depended on Rare to figure it out. That collaboration that Rare had with Nintendo wasn't there with Microsoft, but not because Microsoft didn't care. It's because they were still learning.

From a creative perspective, again, Rare would have been better off with Nintendo. Many people argue about the importance of creative freedom. What we don't about so much is when to intervene and when not to intervene. For the most part, Nintendo left Rare to do what they wanted. Occassionally, Nintendo would step in and intervene. For the most part, it was for the better and the games sold better as a result. With Microsoft, since they were new at publishing, their first reaction was to leave Rare alone. Unfortunately, that collaboration was no longer present. Then when that strategy didn't work, Microsoft then went to the other extreme and started cancelling projects left and right. Under Microsoft's leadership, Rare has cancelled more games than what they have released. 

To be fair though, an ownership under Nintendo or a continued partnership would not have been perfect. Keep in mind that prior to the Microsoft buyout, many talented people had already left Rare. Rare was still understaffed and an investment and expansion of Rare would have been needed. The transition to the 6th generation would have been rough no matter who their owner was. But I think in the long term, Rare would have been better off with Nintendo and all the people who left Rare afer the Microsoft buyout would be there right now. 

Considering Nintendo held their hand in development of their games yes, Rare's decline happened because MS don't baby sit them like Nintendo did, look at Retro they've had talent leave but are still able to maintain quality in their games.

Exactly Nintendo doesn't put up with shit effort. Yes, occassionally a sloppy game will slip through, but the cheerful/cuddly persona of Miyamoto is a myth in development terms, even around Nintendo other devs talk about him more like Darth Vader patrolling the Death Star. If your work isn't up to par, you're going to get it. 

Retro learned this the hard way in their infancy when Nintendo canned NFL Football, a racing game, and Raven Blade and forced them to work on Metroid and then put their feet to the fire to make sure the game was really good. 

Agree to disagree.  There's no proof a Conker sequel would've been greenlit by Nintendo, from a critical and marketing perspective - Star Fox Adventures bombed and didn't move any GameCubes, and creative strength?  Come on.  You can't forecast that.  Nintendo 3rd party input didn't make Geist, Devil's Third, or Die Hard Vendetta very good games - did they.

The question posed in this thread simply can't be answered without a magical crystal ball - and that doesn't exist.

Yeah he's also known for being straight talking when ideas are pitched to him from other developers in the company, most notorious is his trashing of many Zelda builds because of dissatisfaction. ALBW was developed by a younger team because the previous build he saw was not up to scratch so most of the team got axed and sent to other projects while a new team was brought in.

Obviously we can never be sure but I voted "yes" because I think Rare started of decent at Microsoft with Kameo, a game that would have sold much better on Nintendo consoles, and a game like Perfect Dark Zero was quite bad but I think that was also because they adjusted to a more mature xbox view over their original style and a game like that would have still sold better on the wii, with motion control hype around the release.

Now also I think Rare would have done a good job with a lot of Nintendo IP's they could have used and thats deff not the case over at Microsoft.

On the bright side, Sea of Thieves looks good and Rare is on a lift after the worst-period they ever experienced.