The general correlation I've seen is that games with more dynamic physics tend to provide more opportunities for exploits. Jumping, bouncing off of other objects in the environment, rapidly changing geometry (by ducking, dodging, etc.), etc. Being able to trigger "mode switches" in physics (like ragdolling, attack animations, clipping prevention logic, etc.) also helps. Complex AI is also a perennial source of fun exploits. Underflows/overflows are not as common as on older systems but you still see them from time to time.
In that vein, there's a hilarious exploit in Zelda: Breath of the Wild that uses the bullet time mechanic activated by drawing a bow while airborne. Basically, the game drastically slows down time, but the developers missed a handful of physics corner cases that cause acceleration/momentum to be scaled up by the same factor when exiting the bullet-time mode. So with some practice, one can learn to bounce off of an enemy and fly halfway across the map [1].
