Not much.

After Activision bought Bizzarre Creations and then disbanded the company due to blurs poor sales, head developers from that company joined Turn 10, CodeMasters, and Playground Games. So while Bizzarre Creations fell apart, the developers were still around in other company's.

After MS bought Rare and starting making Rare develop Kinect games, a lot of head employee's left to join Crytek.

Similar things would happen if MS/Sony left.

If Microsoft left, things would go back to the way it was before Microsoft joined, just like on PS1/N64, but the gap probably won't be as big. 343 would join Gurilla, Activision or EA, etc.

If Sony left, Nintendo would probably come in and buy various studios and build up 1st party studios. I would bet that most of the Japanese developers would become Nintendo exclusive, and Western developers would either go multiplatform or Microsoft exclusive. Either way, Nintendo would get all of Japans support (like in has on 3DS and it had on SNES), and the Microsoft platform will do well in America's, but it will always be second to Nintendo.

Once a studio has been purchased, there really is no difference between it and a studio created internally.  When you buy another business, you're basically purchasing the assets; after that, they're yours and you can do with them what you want.  I've personally purchased another business myself.  I had the right to everything, including the name, but I instead rolled it into my own pre-existing business.  Sony or Microsoft could do the same if they wished.  Sometimes they do, as Sony has done recently, but they often keep recently acquired studios together, at least for awhile.

If you want to know what would happen, just look at THQ.  It's the same thing, basically.  They were able to sell some wholly owned studios but not others.  Those they couldn't sell were simply closed.  The IPs and games belonged to THQ, many of which they sold individually but some they were able to sell with the studio itself as a package.  If Sony were to close down WWS, for example, they could dissolve Naughty Dog, they could sell it and IPs like Uncharted separately, or they could possibly sell ND with certain IP in a package, depending on what they wanted to do and the buyer wanted.

It's just like if you were to sell your house.  You could sell it with the furniture or without, it's up to your and the buyer.  They could even let go all the employees and sell the "name" Naughty Dog and nothing else, if they wanted.

Well Naughty Dog would be bought up in an instant know doubt in my mind XD easily one of the best developers in the industry and anybody would be lucky to have them 

As Kantor said, if Sony or MS would leave console-business, the other would see increased sales. But game-companies have to find new publishing-routes. Surely Nintendo would profite and get more multiplats. Also we would see more exclusives again. Western developers may move partly back to PC. Japanese developers would be largely unaffected by MS leaving, but would probably move towards Nintendo if Sony leaves. The internal studios may be sold, but they would have a hard transition, would lose staff and may work differently under their new boss.

If they both left it would be a huge change to the industry, but if one of them left, then I don't think it will be too significant. We'd just see a more dominant console. With the lower competition,perhaps we would see less innovation from the one who continues to stay in the industry.
As for the gaming developers owned by them, wouldn't MS/Sony just sell them off?