Such as the fact that 'utf8' isn't 'utf8', 'utf8mb4' is... the feature was in testing as utf8 was being standardized and mysql used 'utf8mb3', and never updated the reference for 'utf8' for compatibility, even across major versions.
There's also the fact that collation on indexes for binary fields are case-insensitive if your default collation is, even if it's "binary".
Also, PostgreSQL has nicer support, imo, for JSON (JSONB) data, as well as a rich extension ecosystem.