Braided wire is flexible like stranded, but the braiding keeps individual conductors in place, as there is no insulation do do that. It's used in places where you don't need or want insulation, such as the engine-to-chassis ground strap. Stranded is just as flexible, and the conductors are held in place by insulation.
The only place I've seen braided insulated wire is in coaxial cable. That consists of an inner conductor surrounded by insulation, then a braided sleeve, and an outer insulating jacket. The braided part has to be flexible but must stay in place when bent and of course in fabrication.