How does controlling in an international environment differ from controlling in a national environment?

It doesn't; it is equally complicated in both environments.

The international environment is more complicated because you have to take into account the more complex labor laws, accounting statements, and other issues the manager has to adapt to$.$

The national environment is far more complicated because there is a lot more responsibility, while in the international environment a large segment of controlling is outsourced.

The international environment is usually more complicated for managers, because they have to do all of the work themselves, while in a national environment you have the help of domestic advisory agencies