In most cases, an ECBO Enterprise Connector deployed locally (on the same system as the Gateway) will have better performance than a JAX-RS Enterprise Connector deployed locally, because the JAX-RS Enterprise Connector must communicate over HTTP even when it is installed locally.
In most cases, a JAX-RS Enterprise Connector deployed remotely (on a different system from the Gateway) will have better performance than an ECBO Enterprise Connector deployed remotely.