Hydroelectric Facility Relicensing Amendments of 1984 - Amends the Federal Power Act to require the Federal Energy Regulatory Commission to issue a new license to operate an existing hydroelectric facility to an existing licensee upon the expiration of the existing license if the Commission does not exercise its right to take over such project, if such existing licensee applies for a new license, and if the plans of any other applicant are not better adapted to serve the public interest. Requires the Commission to issue a new license to the applicant whose plans are best adapted to serve the public interest if the existing licensee does not apply for a new license.