The choice of whether to organize as a nonprofit depends on what you want to accomplish and what sources you expect to tap for your funding. A for-profit theatrical entity aims to return a commercial gain to its shareholders or investors ("angels"). A nonprofit does not. For a theater company, a nonprofit status is just a different way of doing business.
To be recognized as tax exempt by the IRS is a wonderful benefit for most theater companies. It opens up a lot of economic benefits that are not available to commercial theater entities.
This article explains the process, and provides links to additional information.