This gets said a lot but the truth is Rare were under a bit of a downward slope even before MS picked them up. Jet Force Gemini had some game design issues unbecoming of Rare's output at the time, and Conker wasn't as well-received as Banjo-Kazooie. Even Banjo-Tooie, which most liked a lot, was also acknowledged by them as just more of the same. And DK64 got the dubious title of bloatware by some reviewers at the time (even when you play it today you can clearly see areas where they just added stuff to pad the game size and length rather than it being genuine content). All of that happened while they were still under Nintendo.
The idea that they went to shit when MS purchased them is a bit hilarious considering MS also purchased Bungie at the same time or slightly before, and Bungie weren't affected at all. Same for other studios like Bizarre Creations. People just like to use the Rare example as cherry picking, and also seemingly ignore that even though Banjo-Kazooie kind of fell off, Nuts & Bolts still had its charm and the studio started recovering with the Viva Pinata series on 360 (let alone where they seem to be going now with SoT and Everwild, latter being genuinely intriguing for me).