Oh, definitely.

Rare has been in constant decline ever since Microsoft bought them.

Honestly yes, I think Rare would have been better off today if they stayed with Nintendo back then. Rare has become a joke mostly since being bought by MS.

obviously, almost all of the great Rare titles have total 'Nintendo' vibes and Nintendo is known to work closely with contracted second party studios

I believe a lot of the Rare employees actually left after (or during?) the development of Perfect Dark, however there still were talented individuals in the studio. Obviously Nintendo not stepping up to make a big bid on the company makes you think that they felt Rare was heading downhill regardless, especially when you look at something like Star Fox Adventures*...

that said Rare has made pretty much only shit since they stopped exclusively working for Nintendo / were purchased by Microsoft so I think its safe to say that obviously under Nintendo they would have had much more success.

Pretty much all of the Nintendo studios release some level of quality consistently

Nope, there was a exodus of talent that happened as the N64 was wrapping up hence why they haven't done anything besides one or two gems, Rare has been on the decline, not even Nintendo short of hand holding them with their best IP could stop that.

I actually think their decline began before they left Nintendo; their final game for Ninty, Starfox Adventures, was pretty bad and lacked the quality of their prior works, impressive graphics aside.

Frankly, I don't think Rare has made a single good game since the N64.

I can't say fore sure, but I tend to think so. It's been pretty bad for a while now. Only one I ever played thoroughly on XB was Kameo. Finished it and all. Was decent. Perfect Dark didn't really do it for me, and I didn't like Grabbed By The Ghoulies much. To me, their last great game was Perfect Dark on N64.

Does a bear crap in the woods and wipe his ass with a white fluffy rabbit?

Short answer: Yes.

Of course they would, shure, they most likely wouldn't have kept the incredible success they had back in the days today, but they would still be far better than they actually are: When Rare was bought, how do you think the devs that had been there since the beggining felt when they were told that they could never ever again work on Donkey Kong, the game that made them really successful ? Not only that, but Rare always wanted to be indipendent, that's why Nintendo only bought 49% of them, Microsoft came in, threw some money at some people and made Rare their oen thing

IP like Banjo-Kazooie and Diddy Kong would've killed it on the Wii/DS too, and Perfect Dark probably would've done solid if not good sales judging by Red Steel.

Nah, Rare was in decline before Microsoft even bought them out and boy did Nintendo get lucky when shit like Grabbed by the Ghoulies hit the fan since it skipped the Gamecube when it was well over half way in development for it just before Microsoft purchased them ...