Speaking of comparing MySQL and PostgreSQL functionality, I've been spending some time recently on this very topic. Both are great databases with interesting and sometimes unique features. Here are some of the features PostgreSQL is missing as compared to MySQL:
- synchronous multi-master cluster (Galera, Group Replication)
- distributed in-memory grid with automatic sharding (NDB)
- semi-synchronous replication (will be available in PostgreSQL 10)
- built-in logical replication (will be available in PostgreSQL 10)
- built-in event scheduler
- clustered indexes
- declarative partitioning (limited functionality will be available in PostgreSQL 10)
- optimizer hints
- optimizer tracing
- efficient MVCC implementation that is unaffected by XID wraparound problems and VACUUM issues (see also Uber's report on moving from PostgreSQL to MySQL)
- page-level compression
- page-level encryption
- page-level incremental backups
- user variables
- NoSQL client APIs (HandlerSocket, memcached protocol, X protocol)
- virtual columns
- ability to choose data page size on database creation
- ability to specify column order when adding a new column with ALTER TABLE
- write-optimized storage engines similar to MyRocks and TokuDB
All of that may seem small from a developer's standpoint. Those things, however, are huge for people who design and operate the busiest websites on the internet. Which is probably why MySQL still shines in that field.