The significant differences between the two systems are" a herbie is a bottom mounted system, while the BA uses a side mount. A herbie is far easier conceptually but takes up far more space, the BA requires lifting the water through the side wall thus creating an actual siphon, which requires more time before the siphon will "start up".
Neither of which will create any kind of stagnant water and nothing will go rancid. It's when you split the system into different overflows leaving one with just an emergency and the return pipe (thereby no water is flowing through it).
Just a trickly of flow will keep the water clean it's when it sits there with a small film over the top that the oxygen is slowly depleted leading to an anoxic area.