I honestly don't know what the difference is but the number of hops is probably a contributing factor to the decrease in speed. There could be some translation layer happening when going from the CloudSQL instances private IP to public IP with some security checks that slow it down.

I didn't have to worry about the 'ease of connecting' when using CloudSQL as all my GCP services are in the same VPC.

Also, private ip is one less security problem to worry about.

Is it speed of establishing a connection or does it affect pooled connections? What database engine are you using?

We abandoned cloudsqlproxy partially because the sidecar in Kubernetes caused random disconnects, but also because it just had bizarre network errors sometimes. (That was mostly when connecting from outside GCP though.)

We are using PHP and thus no connection pools at all. This definitely doesn't help us with speed. With public IP there was some mystery point that just slowed everything to a crawl.

MySQL for our DB.