ChatGPT is better, but Google owns all of the panes of glass (for now).
We've never seen a "Dog Pile vs Yahoo" battle when the giants are of this scale.
It'll be interesting to see if Google can catch up with ChatGPT (seems likely) and if they simply win by default because they're in all of the places (also seems likely). It'd be pretty wild for ChatGPT to win, honestly.
People are forming deep personal attachments to it. They think all their chat history is in context and Act as if it knows them personally and has formed an opinion about them. They are replacing social interaction with it. I doubt someone in that deep would want to switch to something new very easily.