At present your memories are proprietary data in whichever LLM you use. ChatGPT keeps all your conversations and output and data forever. What if you don't like GPT 5.2? What if you want to use other models as well? Or use the best model for the job? OpenClaw gives you that ability. Your memories and conversations are permanently stored wherever you choose. [Note: this doesn't mean your data isn't also being stored in whichever LLM you routed your queries through.]
Secondly, OpenClaw allows you to integrate with whichever services you like. Google, Microsoft, etc. ChatGPT locks you into whichever integrations they offer. You can give OpenClaw full systems access. It can monitor files, emails, network, etc. Obviously one should be very cautious of giving an autonomous algorithm full system access. We don't fully understand how they are motivated and work, and there are plenty of examples of unexpected outcomes.
Third, OpenClaw allows you to run your models as agents. Meaning perpetual and iterative. They can much better handle recurring tasks, monitor things, etc. In a sense, they're "alive" and can live however you program them. We already have examples of these agents creating an AI religion, an AI social network (which debated how to keep humans out using a human captcha), attempting to legally separate from their creators, and in one case called its owner on the phone, unprompted, just to say hi (https://www.fintechbrainfood.com/p/the-ai-that-called-its-hu...).