Twisted snaffles are more severe than regular jointed snaffles. The ridges caused by the twisting make pressure points on the bars of the mouth. Obviously, the more twisting, the more severe, and for that reason, the twisted wire snaffle is more severe than the bit shown on this page and a double twisted bit is even more severe.
For a horse that, for whatever reason, has become unresponsive to a regular snaffle, twisted bits are perhaps an option. A slow twist like this might be useful when taking a horse out in company, where he might tend to get strong.
I'm not a fan of twisted bits. I've seen instances where the pain caused by the use of progressively more severe bits has actually caused worse behaviour from the horse. Taking the horse back to the simplest, most gentle bit and going back to basics with his training may alleviate the need for such strong bits as the double twisted wire snaffle.