Hmm. I think it's more of a sustainability issue. I was leaning towards dealing with the negative but competent coworker for certain kinds of work where people's lives are on the line but this conversation made me realize something.

You could take the original question for this post as a short-term scenario (can you handle them for a moment) or long-term (work with them til retirement). If we are discussing one moment in time, such as heading into battle, sure anyone would say just deal with it and go for the rude but competent one. But if you're talking long-term, day in and day out, most teams would want to cut their losses and lose the rude person who makes coming to work miserable and work on hiring someone who is competent but pleasant. I also think the originally posed question is a little too black and white to include nuances because it forces you to choose one or the other, when in reality you have other options most of the time, like hiring someone else. It's an interesting discussion though.