I first heard of Vegemite from the 1981 song “Down Under” by Men at Work: “He just smiled and gave me a Vegemite sandwich.”
The song is about an Australian man traveling the world, proud of where he comes from, and how he interacts with the people he comes across who are interested in Australia.
Not surprisingly then, Vegemite comes from Australia; Marmite is originally from Britain.
Interestingly, most of the information I came across on the two food items was primarily by average folk who conducted an unscientific-but-still-valid taste test.