Superfly is based on Blender Cycles renderer. Branched Path Tracing in Cycles is not fully developed, but it does come in handy if you render materials with caustics, like glass. That's about it. It was supposed to reduce fireflies and noise in a render if there were lots of glossy materials with transparencies, like glass materials. But Cycles has no less than 3 different ways to reduce noise in a scene now, and with GPU AI denoising, noisy renders are no longer an issue. I would only use branched path if you want or need nice caustics rendered in the scene. Otherwise, always keep it turned off. Renders will take longer with it on.