Most of us have gone through this bad experience, and learned from it… Almost, then other bag fell off, and so on… This means your still learning, but no matter what you do or what your using always double check everything is secure. On my personal experience I’ve had issues with bungee cords, some were loose, others braked, others weren’t tight enough. This bad experiences made me use no stretch straps. As I’m saying this is my experience doesn't mean bungees are bad, but I will never use them alone again.
For me the most reliable, long lasting and safest of all options are the metal cam buckle straps, but D-rings or the plastic ladder lock straps will also work just as safe. The critical part is how to strap your luggage.
Have you seen how constrictor snake kill their prey? Well that’s how you should strap your bags… Use the strap rolling it one full turn around the bag. This will compress the load and blocks it from sliding. Check that each strap give you secure anchorage points, and the whole load has at least 3 anchorage points. Check out more info on the BOA-Straps seccion