Which type of soap removes more grease, dish soap, or shampoo

Dunno about variables and constants, but I would feel safe in saying that dish soap removes more grease than shampoo.

It is unlikely, barring some unfortunate mishap, that your hair is as greasy as the frying pan and plate used to cook and eat a deep fried meal. Also, with shampoo you have to worry about skin reactions to the user, which you don't have to do with dish soap. So of the two, dish soap will remove more grease.

you need to look up surfactants , or the differences between soaps and detergents