I'm sorry Anchorhead but I have to disagree there.
Star Trek and Star Wars are probably head to head but as far as characters go, most people could probably recognise the main characters of the original show to varying degrees, the Enterprise, a TNG Klingon, Picard and that's it (maybe a Borg if they are young enough).
But most people wouldn't remember what Planet Vulcan looks like (even the matte artists on TMP forgot that one) they wouldn't know a Romulan War Bird from A Klingon Bird Of Prey.
They wouldn't know what an Andorian looks like and while they may recognise the sound of a transporter beam or the look of an OS phaser pistol, they probably wouldn't know who went out with who, what Kirk's son's name was, what Spock's mother's name was.
Most people would be able to describe Tatooine, or Endor or Hoth, give them a torch and they will make a lightsaber noise.
They know Vader is Luke's dad and Leia is Luke's sister. They could probably identify a stardestroyer, a Death Star, The Falcon. the sound of a TIE Fighter (even if they didn't know what it was called).
They know what the Emperor looks like and what he sounds like (just look at the Pope Benedict parodies of him as Palpatine).
They could describe an Ewok even though they are never called that in the film they feature in.
Star Wars is bigger than Trek it's everywhere like it or not.