Modern codes have moved back to 2x4, then they put continuous foam on the outside of that to make the total the width of a.2x6 wall. Wood is not a great insulator and you have to have some
> Modern codes have moved back to 2x4, then they put continuous foam on the outside
Codes do allow for only external insulation, but it it also possible to have some exterior "continuous insulation" with the remainder being in the wall cavity.
The thicker the exterior insulation, the trickier it can be to attach it to the wall and then also have mechanical fasteners for your external cladding.
However, AIUI, using 2x6s reduces the number of studs needed and so would generally reduce the cost on average from both a material and labour perspective (even if 2x6s are slightly higher each).
I should have said modern building and not codes. there are a lot of ways to satisfy good codes, 2x4 tends to be cheapest for single family houses, but others are not far behind and may be worth it in the long run. Consult a proper engineer if you are building a house of course.