pg_embedding is based on a different approximate nearest neighbors algorithm - HNSW, which is generally considered - and studied - to be faster as well as more accurate than pgvectors IVF (ignoring a lot of nuance).
However pg_embedding serves the index out of disk, whereas most vector databases opt to serve the index out of memory, or delegate to mmap'ed files. HNSW is a graph-based algorithm, thus access patterns are random and this does not lend itself to disk based access. I'd expect pg_embedding to be slower than memory-resident indices due to this fact. Also in general with a postgres index, my concern would be scalability and resource isolation. It's convenient to colocate these things but ANN indices have very different CPU/Memory/Disk usage patterns than what you may need for just your relational data.
For example
Chroma -> Serves HNSW out of memory, persists to disk with a WAL.
Weviate -> Serves HNSW out of memory, writes HNSW graph search to WAL and uses that for durability.
Milvus -> Serves HNSW out of memory, supports partial mmap, also supports another algorithm called DiskANN which is optimized for SSD. It uses cloud storage with a shared-everything architecture for durability (a lot of nuance here.)
QDrant -> Has a WAL, supports memory and mmap'ed indices.