I typically think of it this way: use a colon when the second clause clarifies or adds context to the first clause; use a semicolon when the two clauses are related but one isn’t modifying the meaning of the other. To me that’s really the key: the choice depends on how you want to adjust the relationship between the two clauses. It’s a bit like putting different colored lenses over an image to adjust its mood or something.

(Note that I’m talking specifically about using colons and semicolons to join two independent clauses here. There’s lots of other uses for both marks. I also acknowledge that employing some of those other users here is potentially confusing and I apologize for that. It’s just the way I talk. I can’t help it.)