When would you use it? When it comes out to filling out forms where ethnicity is requested, I personally prefer "Caucasian" to "White"; paper is white, not my complexion! (Although I certainly can't trace my ancestry back to the Caucasus.) In modern times, ethnicity or race ought to be largely irrelevent, anyway.
For genealogy purposes, the rule, "use their term" not only promotes historical accuracy, but reduces the area where we can get into arguments about whose personal preference is best!.
So if you're including US Census information and the person's entry says she is "white", then that is what it says, like it or not. You don't change it to Caucasian, because it doesn't say Caucasian.
Racial designators annoy me and I've tended to leave "white" out in reporting that census data. But lately I've realized that African-Americans seeking to trace their ancestors have an immense challenge, and leaving out the racial designators in census reporting can make their job even harder. So I'm re-thinking that.