I personally haven't had a reason to use Oracle's because I like having the latest version and any actively maintained LTS versions available for development and would prefer to use one vendor for all of them. Eclipse Temurin and Azul Zulu are the two I've personally used, but I'm not aware of any technical differences. They should all work the same since they're built from the same code.
Most of the big vendors are running the TCK tests to certify compatibility as well.
Most of the big vendors are running the TCK tests to certify compatibility as well.