Is it impolite to ask to which journal a preprint was submitted?
Yes, I think this question is impolite.  The submission history of an article is usually considered a private matter, because if the paper doesn't appear in the journal where it was submitted, one can infer that it was rejected.  It's a little like asking about their sex life.  If someone I knew well asked me where I had submitted a paper, I might tell them - but if a stranger or casual acquaintance asked me, my reaction would be "That's none of your damn business."   (My actual reply might be a more polite version like "I'd rather not discuss that.")

I suppose that, as Anonymous Physicist says, you could ask Smith if he has any advice on where to send such a paper.  But since you seem to be competitors, he might not be inclined to help you out in this regard - in fact, if he does offer a suggestion, you may not really want to trust it.

It would also be reasonable to contact Smith and propose a joint paper, though of course he is free to decline.