The place I used to take lessons had a few of those kinds of safety stirrups. They also had a lot of peacock stirrups. Never really got to see them in action though, so I can't say if one type is better than another.
I have used the same peacock stirrups for the last 3 years and I love them. They are no different than regular stirrups when the bands are on and I have fallen off and had my foot go through the stirrup with them. The rubber band popped right off and my foot came out. I had no idea that my foot had even gone though the stirrup until I saw the video.