You can see performance comparison to Hydra on ClickBench: https://benchmark.clickhouse.com/ by selecting ParadeDB and Hydra. Tl;dr: It is much faster.
From a feature-set perspective, in addition to querying local disk, we can query remote object stores (S3, GCS, etc.), table format providers (Delta Lake, soon Iceberg too).
From a code perspective, we're written in Rust on top of open-source standards like OpenDAL and DataFusion, while Hydra is their own codebase built from a fork of Citus columnar, in C.
Hydra is a cool project. Hope this helps! :)