My understanding from the developers follow up statements (sorry, I can't find the link) was that the game was basically not getting made without Microsoft making the investment. Despite selling a few million copies of the Tomb Raider reboot across 5 platforms, apparently it made little to no money.
Who knows if Sony turned it down (they aren't flush with cash and already bankroll Uncharted) before Microsoft rescued the franchise? Either way, I don't get the hate. Without Microsoft, there would be no new Tomb Raider. And, at least for me, Tomb Raider started with Microsoft as a DOS platform game. The PSX version was a terrible port of the 3DFX version.
Wouldn't we rather see another great game instead of no game? I hope this means that they've got the cash to make another Sleeping Dogs game now as well. I'd hate to see that series quit at one game. Just buy both consoles, there are going to be great exclusives for both.