Randall White, who has extensively examined the Middle-to-Upper Palaeolithic transition in Europe indicates that it is a matter of degrees, not a sharp break of any kind. Further, recent examinations of the Chatelperronian tool industries of western Europe, which bridge the Neandertal/early modern transition, indicate a very high level of cognition, on a par with modern humans.
What is generally lost in the discussion is that even after modern humans first appear in the fossil record—close to 160-190 kya—tool types don’t become more complex until roughly 100 thousand years later. Further, tool type complexity really ramps up in the Upper Palaeolithic and technology turn-over becomes quicker and quicker.