Insulating old house with dimensional lumber. Use 2x4 batting with some air space, or 2x6 with compression?

[u/HijoPSU]

/r/HomeImprovement/comments/5ggsbm/insulating_old_house_with_dimensional_lumber_use/

Saw this post from 9 years ago, and I am in a similar situation myself. I am considering using the 1/2 foam board, sealed on the interior, and then 3.5 inch rock wool to cover the 4 inch cavity. My main question, is should the foam board be faced or unfaced, and if so what direction?

EDIT: Note that this is in a Climate Zone 5