As ordinarily used, these words are interchangeable: There is no difference between saying "This report is essentially the same as that one" and "This report is substantially...."Each word conveys the idea of "basic" and "of the essence." Adjectival forms do differ, however: an essential service is an indispensable one, such as health care or fire fighting. A substantial service may or may not be indispensable, but it is always of considerable amount, quality, or size."This drive raised a substantial amount of money for the hospital."
Dictionary of problem words and expressions. Harry Shaw. 1975.