There's claims that you do get better gas mileage with premium gasoline but in my experience the gas mileage is the same with either premium gasoline or regular gasoline.
The premium gasoline just costs more and I see no difference in gas mileage. Even if you did get better gas mileage with the premium gasoline you're not saving any money after all by buying the premium gasoline over the regular gasoline since you're paying more per gallon for the premium gasoline.
Unless your vehicle states you really need the premium gasoline then it's best to just stick with regular gasoline which is cheaper than the premium because you likely won't get better gas mileage buying the more expensive gasoline over the cheaper gasoline.