The most significant implications are archeological. Stone tools survive in the record, wooden tools do not. And only stone tools that are modified either by use or for use would be recognized as tools. The big question here is whether or not stone tools that have been attributed to humans ancestors may have been made my chimps, or chimp ancestors.
Is it more intellectually sophisticated to modify stone tools than wooden tools? I don't know how to quantify this. I think the techniques for modifying stones are probably more difficult than just stripping branches and bark. Stripping is a behavior apes already have as they use it in some cases to strip leaves for eating. So stripping to modify a tool could be just the application of one behavior to a new purpose. Modifying stones seems more diffcult - you have to strike one stone with a harder stone. This may have started really simply - splitting a stone to achieve a flat side for smashing, for example. And this may have led to flaking to produce an edge, which requires some technique.
So my sense is that stone tool making is a bit more sophisticated than stick tools, but the most basic modifications of stones are probably just one step up. Of course, stone tool use became very sophisticated among our ancestors, leading up to the homo sapiens stone tool kit that was highly developed - including artistic pieces that would not have been functional.