Brandon had been slowly but surely gathering steam as an action star in stuff like Showdown in Little Tokyo and Rapid Fire, and had he lived, I think The Crow would have finally pushed him into the big time. It got rave reviews from pretty much everyone when it came out, it was financially successful and he delivered a strong performance, easily the best of his career at that point. He had charisma, he had moves, and he had looks. I think it's safe to say he'd have been a major film star had he lived.
Incidentally, Jackie Chan may be the biggest Asian movie star in America, but he's not the only one. There's also Jet Li, Chow Yun Fat, Lucy Liu was a movie star before she went to TV, Mako (RIP), James Hong and Cary-Hiroyuki Tagawa are all popular Asian character actors, all with careers that span multiple decades, of course there's George Takei.