Reubens - Sauerkraut or Coleslaw? [Split from Pacific Northwest board]

[Split from this thread: http://www.chowhound.com/topics/486423]

I have a question for Reuben afficionados. I've always had a Reuben with sauerkraut, but my girlfriend, who grew up in Jewish delis in New Jersey has never even heard of such a thing. She says that a Reuben has coleslaw, not kraut. I recall, also, reading in a James Beard book, his lament about how nowadays (the 40s, I believe) people are making pastrami sandwiches with sauerkraut instead of coleslaw and calling them Reubens. What's the story here?