The middle stud of the three-stud package within the four stud illustration is always scraps of wood, not a full stud. So both are three-stud corners in actuality, the bigger one is just more nails/labor.
A modified cali corner uses ladder blocking on the left side instead of drywall clips; still allows for better insulation properties, but makes the corner more solid.
I personally like to use ladder blocking at p-posts as well, to cut down thermal bridging. And it makes it easier to plumb up the partitions, and fewer precision measurements required at a point in time where you have so may things to do to get the house to dry-in.
Casey

The builder is partially correct.

It may be easier to frame without errors because that is the way most framers learn to frame so you do not have to get them to change how they always do it.

Technically it is not harder to frame a California corner or there is so little difference that it is not really an issue.

You are probably correct that it will not require a large amount of additional money to heat and cool the house.

I would be concerned that the builder seems to be disregarding the specifications. What are the implications of this for the whole build? Does this mean that they really do not care about energy efficiency?

I'm with Chris.

Let the builder construct stud walls the way he is used to. Since you have external rigid insulation to prevent thermal bridging, you have nothing to be concerned about.

Pick the battles that are truly important. Monitor the construction to ensure the documents and specifications are being followed for the really important stuff.

Good luck on your project.