I could see a Venn diagram being drawn in which there's a circle for Star Wars, and a circle for Batman, and where they intersect it leans heavily into Batman. But I think the Star Wars circle is much larger than the Batman circle.
There have been exactly 3 live action movies (not counting 66) in which Joker has appeared. That may be changing with Joker solo movies now underway. But his appearance in those movies do not, I think, really approach the financial success or cultural impact of Han Solo in any of his 8 appearances.