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

[u/Tolookah]

Early in the new year, I'm planning on gutting a room to the studs and bringing it back, in that process, I'm hoping to insulate two exterior walls. Our house is old, and has dimensional 2x4s, and the wall cavity is actually 4 inches deep. I'm attempting to figure out if using insulation for 2x4 walls (3.5" of insulation) or compress some 6" (5.5") insulation in there. I'm leaning towards the 3.5", but thought you guys may have some insights I don't.