In a comparison of performance between PostgreSQL and ClickHouse databases using real-world data from YouTube, ClickHouse outperforms PostgreSQL by 5-10 times on average, with one specific case showing a 20x improvement. The results highlight the importance of choosing the right tool for specific use cases, as each database has been designed to excel in certain areas. In this particular instance, ClickHouse is better suited for handling large datasets and column aggregations, while PostgreSQL struggles to keep up.