The MySQL manual says that INNODB 'adheres closely' to the ACID model, though there are settings where you can trade some ACID compliance for performance.
I've been running PostgreSQL for a client since 2005, we're on our 5th hardware platform in that time period. We also run a MySQL/MariaDB database to support our website, it is currently on an AWS RDB server which is refreshed from the PostgreSQL server. I also administered an Oracle system for a well-known educational publisher for about 10 years. Given my druthers, I'd take PostgreSQL over either Oracle or MySQL.