Not sure what its called but they built their own engine from the ground up in DBC 14 and continually modified it through each iteration. Personally, I'm with Jerm, Unreal Engine is awesome, but a few factors hold it back (as mentioned earlier), namely, steam take 30% publisher revenue and another 10% on that for Unreal - hence why its probably not tangible to use it without moving to the Epic Store (which I despise). I think they'll just keep working on the engine they have now, or perhaps build from the ground up again (not sure if two years is enough time though).
I think the biggest improvements visually I would like to see is lighting, menu lighting is way better than in-game, and skyboxes. Secondary, more animated faces, accuracy is great but they're so lifeless.