Google really doesn't share much publicly except for papers and preset tech demos.
However we know they have been working on AI longer than OpenAI, with better datasets than anyone, with top shelf talent, essentially infinite funding, custom hardware, and what we do see publicly is incredible.
It's a pretty safe bet that Google is ahead of the pack, perhaps even with some distance, but it's not yet clear what they intend to do long term with their projects. What is clear is that they don't want or need the public playing with it.