Who decides on a green card application?

Is it always the same person?
No, it depends on whether the applicant is filing from outside the United States, or from within the United States.

Who is making the decision when the applicant is filing from outside the United States?
The consular officer does. He or she is an employee of the U.S. Department of State, working in a U.S. embassy or consulate abroad. The consular officer is the face of the U.S. government in a foreign country and helps U.S. citizens who are traveling, living, or conducting business abroad.

Who is making the decision when the applicant is filing from within the United States?
The adjudicating officer does. He or she is an employee of USCIS.

Is the decision final?
Applicants who are filing from outside the United States still have to be admitted by an agent of Customs and Border Protection (CBP) who has the power to deny them entry.