No, they're not.
They just have better PR. They're both for profit companies with their share of controversies, but Google just has better PR.
Moreover, Google supported its "responsible" positions by carbon-neutral engagement, retracting from Chinese market, stopping mining email data, and more. I don't really understand why you would describe this as PR, if so then every decision is PR, and in this case "good PR" would amount to "good decisions" and I'm fine with that but not with the pejorative stench of the word PR (and because for most people it does not mean "decision").
It's banned on china.
https://sustainability.fb.com/
No proof on privacy issues but certainly neither seem saint.
Any other concrete examples?
It seems to me that FB is still a little short on ecological engagements. At least, compared to Google.
So, room for improvement.
About privacy concerns, for example: FB is not guaranteeing anything about not mining your private messages. What I find when googling it does not reassure me neither.