Are cyclists safer on roundabouts with or without cyclist priority?

Several SWOV reports and a memo by DTV Consultants show that cycling on roundabouts without cyclist priority is safer than on roundabouts with cyclist priority. At the arms of  roundabouts without cyclist priority, cyclists have to give right of way to motorised traffic, while at the arms of roundabouts with cyclist priority, motor vehicles have to give right of way to cyclists. For substantiation, see SWOV fact sheet Roundabouts and other intersections.