If you use the same insulation - you need a Vapor barrier on the studs, then sheet rock. The Plastic vapor barrier will help keep condensation/moisture from moving through the wall. Watch a couple youtube vids on the subject. In new construction, there are better ways to address the tempering zone where warm meets cool and condensation could form - but, you have what you have so, plastic stapled and tape sealed on studs with sheet rock over that.

If you want to bring up to code - get all those wires secured and up to code standards while you are at it and the wall is opened up. . . .