Nest or Ring doorbell and why?

Giving the gift of removal of privacy for your neighbours and anyone within sight line of the thing? Pfft.

Neither. I don’t want my unencrypted video and audio going to a third-party that is more than willing to turn it over to government or use it for advertising.

Both are trash products - surveillance cameras branded as doorbells. If you didn't need a surveillance camera before you probably don't need one now.

Neither. My data stays in my home or on my server.

If they already have a Nest thermostat, then clearly Nest doorbell since you can use the same app to check both devices. Personally, I think the Nest doorbell looks a little nicer, too.

I heard Google fucked up Nest big time

Never nest. It's a scam, plain as day.