I am no source of authority on this, but on blogs, I see folks generally placing in the aside short & simple eye-catching, summarizing, provocative, or just interesting stand-alone elements. While footnotes receive citations and/or longer digressions.
I feel that this is motivated by the fact that asides are higher up and more visible, and so they might be used to catch the attention of the reader. Footnotes are more hidden away, and so seem to be used to store info the author wants to include in the article but distracts from the main text's pacing.