For me the ones that work are held on the handle bars by velcro - very secure and don't seem to shake as much. Also useful to detach and use for shaving etc. Plus if packing easy again to remove.
Having said all that I use drop bars and fasten it on the lower part so have no idea if they work on straight handle bars.
I would always recommend a mirror as IMHO they are the most important thing for keeping me safe. Having just crossed Oz and ST I had to constantly gauge if two vehicles (especially the road trains)were to pass each other near me and enable me to get off the road.