I've largely found codex and claude code to be about the same however, codex tends to "think" harder and for longer which depending on the task, yields better results without too much steering.
On an unrelated note, UI is such a personal preference that it's impossible, beyond core pillars that have been studied for decades, to say one is better over the other. That being said, I like OpenAI's design system much better than Anthropic. OpenAI products (cli and chat ui) "feel" nice and consumer focused whereas Anthropic's products feel utilitarian and "designed for business".
On an unrelated note, UI is such a personal preference that it's impossible, beyond core pillars that have been studied for decades, to say one is better over the other. That being said, I like OpenAI's design system much better than Anthropic. OpenAI products (cli and chat ui) "feel" nice and consumer focused whereas Anthropic's products feel utilitarian and "designed for business".