Four plank fencing will have less spacing between the planks and also less between the ground and bottom plank -- which makes a more substantial containment. Also, if you plan to have smaller animals or young animals, the smaller spacing will be safer.
We went with three plank and it is one of my biggest regrets about our current fencing. It's all well and fine for our TB, but when we brought home our mini it became an issue. We only have one run of plank fencing (facing the house), so it wasn't a big deal as I just ran a line of hot line across the bottom between the bottom plank and the ground -- now instead of having 23 inches from the ground to the bottom of the fence we have a wire 12 inches up that keeps anyone from getting any ideas about going under the fence.
From a non-containment stand point, it will also provide more of a barrier between things outside your pasture and your horses.
From an aesthetic POV, I prefer the look of four planks - it looks more finished to me.