Great question Immountain!

Evaporated cane juice is juice extracted from the sugar cane plant and then crystallized through evaporation, while sugar has it's juice filtered to remove some of the brown solids. Some of these solids are processed further into molasses. Both of these sweeteners are nearly identical: They both are disaccharides (disaccharide means "two sugar" called sucrose consisting of about 50% glucose and 50% fructose.

Evaporated cane juice has trace amounts of the solids left over but not enough to make a difference in your health. It's marketed as being more healthy but I believe these marketing efforts are deceptive; it's still 50% glucose/fructose any way you slice it. Since these sweeteners are basically the same thing, you should be able to get away with a 1 to 1 substitution compared to white granulated sugar.