While there is likely to be overlap between the various advertising/tracker lists and Privacy Badger, regardless of whether you enable learning locally, Privacy Badger can automatically discover new trackers that list-based blockers don’t know about.
Besides automatic tracker blocking, Privacy Badger comes with privacy features like click-to-activate replacements for potentially useful trackers (video players, comments sections like Disqus, etc.), and link cleaning on Facebook and Google.
Privacy Badger is also a political tool. By using Privacy Badger, you support the Electronic Frontier Foundation [1]. Privacy Badger sends the Global Privacy Control [2] signal to opt you out of data sharing and selling, and the Do Not Track [3] signal to tell companies not to track you. If trackers ignore your wishes, Privacy Badger will learn to block them. The idea isn't to block all advertising but rather to promote a better Web.
[1] https://www.eff.org/ [2] https://globalprivacycontrol.org/ [3] https://www.eff.org/issues/do-not-track