18v can deliver approx. (18^2)/(12^2) = 2.3x the power of a 12v drill.
For a 1/4", 4" lag screw into a pilot hole into a 2x4 you might need 15 lb-ft (180 lb-in) of torque.
BTW, ft-lb is energy, lb-ft is torque.
You might want to get a hammer drill - I certainly should have. You need special bits but it goes through masonry faster.
You pay a lump sum for the drill but batteries will be a continuing cost.
Taking the first two batteries from
as an example
the first gives you
14.4v x 3 Ah = 43 W-h for $22 so you pay about 50 cents/W-h
and the second gives you
36 W-h for $44 so you pay $1.20/W-h
Seems like the first is a better buy, assuming reliabilities are equal.