In a nutshell, we use both in UKV. simdjson is faster for read-only operations, but it won't help you create a new JSON. yyjson is the best library I have seen for creating/updating JSONs.
If you're primarily targeting Python as an application layer, you may also want to check out my msgspec library[1]. All the perf benefits of e.g. yyjson, but with schema validation like pydantic. It regularly benchmarks[2] as the fastest JSON library for Python. Much of the overhead of decoding JSON -> Python comes from the python layer, and msgspec employs every trick I know to minimize that overhead.