Framing the exterior walls with 2 x 6 studs instead of 2 x 4 can definitely add to the price of the home. In addition to the cost of the lumber, you also have an increase in the labor, insulation, window and door trimming.
The advantages for using 2 x 6 in the exterior walls would have the additional structural strength to the building and the ability to use thicker insulation in the walls.
One of the only reasons I can think of for using 2 x 6 on your exterior wall would be the installation of thicker insulation. 2 x 4 walls will insulate with R-13, which is about 4 inches thick and 2 x 6 will insulate with R-19, which is about 6 inches thick.
The additional 2 inches will be a 50% increase over the 2 x 4 wall. 50% is a lot, dealing with anything. Imagine if you got a 50% increase in your annual pay this year. This would not be anything to complain about, would it.
2 x 6 also has advantages when you are drilling holes for plumbing pipes, electrical wires or heating ducts. Often plumbers and electricians drill large holes in 2 x 4 walls, taking a little bit further away from the structural strength of the home. Some plumbing pipes for example are 2 inches in diameter, drilling this whole through a 3 1/2 inch 2 x 4, only leaves you three quarters of an inch on each side if the whole is drilled exactly in the center.
Drilling a 2 inch hole in a 2 x 6 will leave you an inch and three quarters on each side. In other words if you subtract 2 inches from 5 – 1/2 inches, the thickness of a 2 x 6, you still have a 2 x 4 left over. 2 x 6 framing also gives you 50% more lumber and structural strength in the home. Again this might not sound like much but it is a lot.
If you live near a busy road or highway, you could use the 2 x 6 framing, only on the exterior walls that separate your living area from the noisy road. The thicker the wall, the tougher it is for the sound to travel through it.
The biggest problem with most home builders is the additional cost and this is coming right out of their profit. Most homebuilders, especially the larger ones, depend on every penny they can to survive in the long run. It's an extremely tough business to be in.
If you're building your own home, give some consideration to using 2 x 6 if you live in areas where the temperatures are extremely cold or hot. One of the only reasons to frame the exterior walls with 2 x 6 is the ability to use more insulation and this would cut down utility costs. If you live in a moderate climate, where utility bills are not astronomical, it would not be cost effective, for you to use 2 x 6.