Couple points:

(1) ChatGPT has the first mover advantage

(2) ChatGPT has Microsoft, and they pumped $10B in it (for now).

(3) Microsoft search is better today than Google search, which, while more well known has become cluttered with ads. Try a side by side comparison.

(4) Google has the years of investment in AI, but they have also steadily become risk-averse.

(5) Microsoft went through it's risk-averse period in the 90's-2000's and was basically forced to reinvent itself, they are reaping the benefits of that decision.

So, Microsoft has the "bias to action" advantage here, but Google is hardly far behind.

The winner is the user - because monopolies eventually cause laziness in corporations and a downgrade in quality.