They aren't opposites, but they aren't orthogonal either. Past some point, you have to choose one over the other. I think most designs are far from that point, though - they could easily improve information density by an order of magnitude while still remaining pretty.
It becomes a lot harder to get it right as more visual information is added. Tufte is an excellent source for design guidelines on information density. It is important to keep in mind however that Tufte focuses primarily on static visual representations that people can spend time on, and that do not update.
