Homeland Security Grant Coordination and Simplification Act of 2003 - Amends the Homeland Security Act of 2002 to establish an Interagency Committee to Coordinate and Streamline Homeland Security Grant Programs that shall: (1) ensure coordination among the Federal agencies that provide funding or other assistance to or for State and local law enforcement agencies, fire and rescue operations, medical and emergency relief services, and State and local homeland security efforts; (2) eliminate duplication of requirements contained in emergency plans requested by Federal agencies; (3) simplify and coordinate applications for homeland security funding; (4) identify ways to streamline the process through which Federal agencies support community-based law enforcement, fire and rescue, and medical and emergency relief services; (5) collect information regarding State and local initiatives to promote interoperability of equipment; (6) develop coordinated plans to provide technical assistance to States to promote interoperable equipment; (7) provide coordinated assistance to help State and local governments prepare risk and vulnerability assessments; and (8) review State plan submissions to ensure that all relevant Federal interests are protected.