During the panel at PAX 2012, Hideo Kojima talked about the Fox Engine, and the team’s goals.
There are a lot of great game engines, but they wanted to be able to tweak the engine to their specifications. The goal with Fox Engine is to make things more efficient and easier. As they make the game, they are adjusting the engine to their needs. It’s not a genre specific engine, and what Kojima is trying to make with it right now is an open world game (Metal Gear Solid Ground Zeroes).
The most exciting thing about Fox Engine for Kojima Productions is that it’s their own engine, so they can tailor it to their own specific needs. While developing Ground Zeroes they have various requests to the tools team. So the engine is still improving even at this stage.
Kojima Productions are working on next generation hardware as well with this engine, and it will look very, very good on that.
Source: Hideo Kojima Introspective at GameSpot.