As Walesmaven said, there is no tax advantage. You can - and should - deduct the mileage regardless of whether you file as an individual under your SSN or as an LLC. In both cases, you use a Schedule C to report self-employment income. What changes is the name on the form and whether the name is associated with an SSN or an EIN. I actually file a Schedule C under my name and SSN, and another Schedule C under my LLC and EIN.
Shopping Southeast Pennsylvania, Delaware above the canal, and South Jersey since 2008