The U$.$S$.$ Solicitor General has an advantage in seeking certiorari, which means that

The Supreme Court is more likely to take up a case if the Solicitor General requests it$.$

A case is more likely to be elevated from a state court to a federal court venue.

The U$.$S$.$ Government is likely to be successful in asking for a lower court decision to be overturned.

The D$.$C$.$ Court of Appeals is more likely to follow precedent where the Solicitor General argues that it governs.