This is off base from the main discussion here, but I did a few basic experiments of my own for mean-field vs full-rank ADVI earlier this year: https://gist.github.com/ColCarroll/d673a3af7169bd713bcbdb9445d4a543
Dan Lee, and then Dan Simpson, hopped in a discussion about it as well, which I found helpful: https://twitter.com/colindcarroll/status/967078763384201216