PostgreSQL provides more tools and builtin features around security, eg: row level security and the support of SELinux (through SE-PostgreSQL). Overall, whatever you choose, the important is to keep it updated and have the skills to apply security best practices and update them regurarly, without this, it's like putting your money in Fort knox but leaving the vault key in a public place.

It is open-source and more tools than mySQL. PostgreSQL is an object-relational database management system (ORDBMS) with an emphasis on extensibility and standards compliance. It is also good for small companies due to tools for free availability. PostgreSQL includes built-in support for regular B-tree and hash indexes. Indexes in PostgreSQL also support Expression & Partial Indices ( index only a part of a table). Expression Index can be created with an index of the result of an expression or function, instead of simply the value of a column.