I'm assuming you mean local logging of your location, as opposed to burying it in a company's blackbox of a cloud. I think it's a far superior option from a privacy standpoint because you are in control of whether or not that information exists to the rest of the world. That is the critical differentiating factor.

I'm also assuming here that you are actively looking to have your location logged -- something most people do not explicitly sign up for before it starts happening for them (usually after it has manifested results, people accept it as some weird fact-of-life).