To explain your examples...
Halo is a Microsoft franchise and an exclusive to the Xbox family, because it was developed by Bungie (who Microsoft used to own) and is now developed by 343 Industries (which is a subsidiary of Microsoft) and the franchise is published by Microsoft (which is to say that Microsoft pumps money into the game's management, distribution, marketing, etc.). Microsoft also owns the rights as far as I know.
Now, with Gears of War on the other hand the developer, Epic Games, owns the rights. But, Microsoft puts up significant money to publish the game - and by extension keep it an Xbox exclusive. Microsoft isn't going to pay to distribute it on a rival console. But, again, Microsoft doesn't own that franchise and Epic Games can go elsewhere if Sony wants to offer the cash. Or ditch exclusivity altogether, it is their call. But, clearly they see more of a financial benefit to sticking with the 360. It comes down to what lines their pockets, not what gamers want. They are a business.
God of War is developed by Sony Computer Entertainment. This would be the equivalent of Mario and how Nintendo develops those games. So, that's why it is a Sony exclusive. For Killzone, it is developed by Guerrilla Games - which is owned by Sony. Much like Microsoft with Bungie or 343 for Halo; or even Nintendo and Rare (way back in the day) or Retro.
The reason is simply money and market share. You said "Not Nintendo", but it is like Nintendo. Nintendo, for all the flack it gets about hardware, has franchises and properties that draw audiences in, sells a ton, and makes them oodles of money (which is the point). They own these franchises. This is the inherit value of the Nintendo company; of their brand. This is what they see as an advantage and why their games are exclusive to them. Similarly, Microsoft has Halo. This is their bread maker. A new Halo game is a guaranteed success. They will make money. No risk, all reward. And Sony has Gears of War and such.
All same. Have exclusive properties that people we continually buy and want so much that they'll buy your console for over another one. If they have only one console and they've picked yours, well congratulations you've just secured more money out of that customer.
That's why there a time or limited exclusives. That's why some platforms have additional content or DLC included. The first-parties (Microsoft, Sony) pay the publishers for these benefits to give them a competitive advantage over their competition and make more money. If the developer sees this as being more profitable than having it released on multiple platforms at once - then they'll stick with. I'm sure the do some analysis. Cost, risk, benefits. How much do they stand to gain for going exclusive? How much can they lose? Does whatever Microsoft of Sony offer them more than make up for it?
In the end, the developer will most likely do what is in their financial interests