Will a mud terrain tire get the same gas mileage as an all terrain tire if they are the same size, weight, etc?

will a mud terrain tire get the same gas mileage as an all terrain tire if they are the same size, weight, etc? I have a 2010 fj cruiser with 16 inch rims. The tires are BFG rugged trail 265/75/16. I was thinking of getting mickey thompson baja mtz in the exact same size but I don't want my gas mileage to suffer just for a different look.