The Big 12 is going to survive as long as the Longhorn Network and Oklahoma have nowhere else they want to go. It will keep its BCS auto-bid as long as the Fiesta Bowl exists and agrees take its champion every year. It's not on completely stable ground, but it's at least stable-ish.
The Big East is on considerably shakier ground with two teams soon to bolt to the ACC (leaving it with six football members) and no BCS bowl tie-in. That plus geography and history make it likely that TCU will spurn the Big East it was set to join and go to the Big 12 instead. CBS even has sources saying "it's a done deal", though nothing has been made official just yet.
With Missouri shopping itself around, it's not certain that the Big 12 will have ten members next year. However the step of adding TCU indicates it will continue to exist whether the Tigers leave for the SEC or not. CBS says the conference would likely expand to 12 if Mizzou does bolt, with Louisville, BYU, West Virginia, and Cincinnati as likely candidates. As an aside, I sincerely doubt that TCU joining the Big 12 will play a factor in Missouri's decision making process.
Whatever the case, the future of the Big East as a football conference looks more tenuous than ever while the Big 12 appears to be a survivor for now.