I'm trying to decide on the best approach to insulating a basement
wall. I'm currently contemplating the following:

Option #1:
Use 2 inch polystyrene foam insulation directly against the exterior
walls and tuct tape it to seal it. Erect my 2x4 stud walls against this
and drywall. Also, I could potentially insulate between the 2x4 walls
with regular bat insulation to increase my R value.

Option #2;
The old way, as defined by a contractor I spoke with. Lay out tar paper
against the exterior walls. Erect my 2x4 stud walls against this. Fill
the voids with bat insulation and vapour barrier the wall. Put up the
drywall.

The first one obviously appears to be the warmer but is it more
overkill ? I'm a little concerned about the loss of real-estate due to
the added wall thickness but the extra heat & potential energy savings
do sound appealing.

thanks,