Both must be done well in order to build a compelling engine. These are handled very differently. The static world. Can be preprocessed very effectively. Is compiled into a single BSP tree.
Leaves are the convex volumes that nodes carve the world into.
A BSP tree performs a convex, hierarchical partitioning of space, with each node defining a subspace that contains all of the node's children. Hierarchical partitioning helps greatly in large-scale culling. Node bounding boxes can be clipped to the view pyramid. If a node's bounding box is trivially rejected, all its children can be rejected with no further testing. If a node is trivially accepted, all its children can be accepted with no further testing.