That seems to be a builder's choice around here. Styrofoam, celotex, etc used to be more common but now osb is used most but some use it. There is a little cost difference but osb is more solid and styrofoam has a better insulating factor.
He is right that if you use it, then you should box the corners with osb (nailed every 6") to help stop racking in high wind situations. The metal cross braces also help avoid racking. Sounds like the builder knows his stuff cause I see some put in on without proper corner bracing.
R-13 is the best fiberglass you can get into a 2by4 wall. Adding the styrofoam gets you another 2 or 3. If you want the insulation value, then use the styrofoam. If not, and you want the solid osb sheeting, then use osb. Whichever you use, put tyvek on it. What part of the country are you from?