There has been an ongoing debate about energy efficiency of exterior walls (2x4 or 2x6), which is better? In terms of wood used, if both have the same stud spacing, the 2x6 obviously uses more wood. But if you can go up to 24inch on center for the 2x6 walls, it is about the same volume of wood used. (About 1/3 less due to spacing, but 1/3 more due to thickness). Some drywall installers complain, but there is no problem here, sheetrock does just fine with 24inch spacing of studs.
In terms of R-value, 2x4 will get you between R-13 and R-15 for most cavity insulations, and 2x6 can give you R-19 to 23. From an insulation standpoint, you're obviously better off with the higher R-value. Another option is to use 2x4 walls but apply a rigid foam board to the exterior sheathing, thus upping the R-value of a 2x4 wall to about R-18. This can also be done for 2x6 walls, giving you a new R-Value of about R-24. There are some considerations when using exterior foam board that relate to attachment of your siding so be careful. Advantage Development Co. is an award winning builder here in Asheville always ready to discuss design considerations with our new home clients. Visit us today at http://www.advdevco.com/ to learn more.