It's been some time since I tried them (a shared kitched had four different -mite spreads), but I remember Marmite being sweeter and softer/less thick, almost syrupy, and a quick search confirms that's what others have said.

"Marmite is saltier, and the spread has a smoother texture. Vegemite, on the other hand, is more bitter with a more robust umami flavor." - (chefsresource.com)