The phrase can be interpreted as having an implicit as (as much as instead of much as), and read as
If aliens ever visit us, I think the outcome would be the same as when Christopher Columbus first landed in America, which didn't turn out very well for the Native Americans.
Which is a relative pronoun used to for something previously mentioned; in the example, which refers to when Christopher Columbus first landed in America.
The sense of the sentence is that the outcome of aliens visiting us would be the same as when Columbus first landed in America: it would not turn out very well for us.