I think kdbush should always be faster for points — it uses more than 2x less memory, because when you encode points as bounding boxes, you basically duplicate them. Indexing and search is faster mostly because you operate on less data.
BTW, the readme of kdbush and flatbush don't mention each other. Might be nice if they do and clarify how they compare.
(because sometimes, people have an older, not updated library, for example)