Believe it or not, it really wasn't Microsoft's fault.  When they bought Rare they made very few internal changes, but the problem was that Nintendo had always been a guiding influence and one of the big reasons Rare games were so good (you see this with a lot of 2nd party Nintendo developers).  Without Nintendo, Rare just wasn't as good at making games.

I remember reading a pretty interesting article on Rare and the take home message from it was that the company were the masters of carteridge development, but those years mastering N64 technology meant that they were a long way behind when they eventually made the shift to disc. Indeed, their struggle developing for the Gamecube is well documented and it's like the company never really recovered from there.

From memory they was starting to lose key staff even prior to the MS acquisition, although it certainly didn't help.

Rares employees from the Nintendo times left rare after MS bought them. Its not the company name that makes good games its the people behind it. If MS buys Rockstar and throws out every single employee and hires a couple of janitors to make new game the result would be shit too.