Can EXIF metadata prove one image is a Photoshop edit of another?

Any metadata can be altered quite easily, therefore slightly sophisticated forgery may alter the metadata such that it looks more original than the actual original. It isn't difficult for instance, to forge the job id of photograph.

However, supposing that the metadata is just one out of many other evidences, the state of the metadata of a photograph can act as a supporting evidences. In your example, the quality of the photograph and that the supposedly photoshopped image is cropped smaller form a much stronger evidence than the metadata. A more direct evidence though, it is supposedly impossible for an outsider to alter the posting date on the Facebook post without leaving edit trails in Facebook's system, unless Facebook is part of a conspiracy to cover up "some unwanted, leaked image".

Whether this type of evidence will be good to establish beyond reasonable doubt for legal purposes, you need to ask a lawyer.