The Docker logging driver and delivery mode chosen by developers significantly impact the performance of their containerized applications. The json-file driver, which writes logs to a local file on the host where the container is running, is recommended for most use cases due to its speed and reliability. However, developers can choose from various drivers that forward logs to remote endpoints or use logging driver plugins to create custom solutions. The delivery mode, which determines how the container prioritizes logging operations relative to other tasks, also affects performance, with blocking mode potentially introducing latency and non-blocking mode ensuring high volumes of logging activity don't impact application execution. By selecting the appropriate logging driver and delivery mode, developers can optimize logging reliability and application performance, making it easier to monitor and analyze their containers' logs.