At this point Google is offering nothing which comes close to ChatGPT, Bard is a laughing stock compared to it. But I don't doubt that Google will catch up and then offer a better experience.
The only thing OpenAI has from me is that (valuable) chat history (and the monthly subscription money), so I wouldn't have any problems with moving away from them once they are no longer in the unique position they're currently in. This is different with Google, which has several orders of magnitude more data about me and which they also do manage for me.
I'm concerned that it's only a matter of time until OpenAi gets hacked and some of the user account's data gets leaked.