PostgreSQL is an object-relational database management system with an emphasis on extensibility and standards compliance.PostgreSQL also supports many NoSQL features as well.
MySQL is an open-source relational database management system (RDBMS). Just like PostgreSQL, and all other relational databases for that matter, MySQL uses tables as a core component and has more-less the same feature set as PostgreSQL.
MySQL will be ideal for your project if you require a high-security RDBMS for web applications or custom solutions.PostgreSQL will be ideal for your project if your requirements revolve around complex procedures, integration, intricate designs and data integrity, and not around high-speed and ease of setting up.