I've seen Episodes 1-6 of Star Wars as well as some of The Clone Wars and Rebels series. That said, I haven't watched any of the modern movies and would only be interested in checking out some of the shows.
On the flipside, I've never watched any of the various iterations of Star Trek that have come out throughout the decades. I've seen bits of episodes of the original series, seen like an episode or so of the animated series on a bad movie stream I used to watch, and know a few general things like Captain Kirk, Spock, "Live long and prosper" and the associated hand gesture, "Beam me up, Scotty!", "KHAN!", Captain Jean-Luc Picard, The Borg, The Enterprise, Klingons, and some of the alien species like the Gorn.
Star Wars wins by default due to me actually having substantial experience with it. I am interested in checking out at least the first two series of Star Trek and the associated movies at some point in the future, so my opinions might change eventually.