As an update - I tried Public IP and same latency issues. It's quite hard 
to diagnose where this would be but I assume the networking between GAE and 
Cloud SQL seems hamstrung somewhere along the line, public or private.

I did however bump the app.yaml config up to F4 instead of F1 and that 
halved the response times and halved the pg times (execution+fetching). I 
expected resource bumps to improve my apps performance but I didn't expect 
it to have that much of an impact on querying and fetching for a machine 
and Cloud SQL instance under no load (executing 1 request every 30 seconds 
only during testing).
The F4 specs seem to put it on par with what Cloud Run fires up, but the 
reason I was interested in GAE is I don't think I should require those 
specs and I'm not talking about a significant amount of data coming back 
from PG (20-40KB).

So I think my question now shifts to is that expected for GAE? Is there 
much more of a tight link between CPU and network speeds than I was 
expecting or am I seeing something strange here? 
At the moment it probably rules GAE out for me and I'd stick with Cloud Run 
or have to bump up my instance class to B8 to get similar performance.
On Friday, October 30, 2020 at 5:56:24 AM UTC+11 amit...@google.com wrote:

> Hello,
>
> By going through the details you provided and relevant documentation for 
> the settings [1,2], I believe the configuration for both are same. During 
> my research, I am yet to find any reason to believe that App Engine takes 
> more time for the connection. Just wondering, are you able to test it using 
> the public IP? Did you find any connection drop from App Engine in the 
> logs?    
>
> [1] 
> https://cloud.google.com/sql/docs/postgres/connect-app-engine-standard#configuring
> [2] https://cloud.google.com/sql/docs/postgres/connect-run#configuring
>
> On Thursday, October 29, 2020 at 10:20:22 AM UTC-4 jonmiddl...@gmail.com 
> wrote:
>
>> Is it expected that AppEngine Standard performs significantly slower than 
>> Cloud Run when a connection to Cloud SQL (Postgres) is involved?
>>
>> Testing whether to move away from AWS and which GCP solution to move to 
>> and have fired up instances of Cloud Run and AppEngine to test a NestJS API.
>> Having added logging to isolate just the time taken to query the DB as 
>> part of an API call, the same GET request that takes 400ms query time on 
>> average in Cloud Run takes 2100ms in AppEngine.
>> To clarify this is the same source, same build deployed to both and these 
>> are the times once warm so I'm excluding the first few requests.
>>
>> For any code not talking to my Cloud SQL instance, i.e. a dummy 
>> javascript method to chew up some CPU time, the performance is more or less 
>> identical
>>
>> Cloud SQL, AppEngine and Cloud Run are all set up in the same region 
>> (australia-southeast1), and connection from GAE and Cloud Run to Cloud SQL 
>> is for both via Private IP and Serverless VPC.
>>
>> Since I'm in free tier whilst trialing my options, I tried chat support 
>> and basically got down to (verbatim) "cloud run is design to handle data 
>> from apis with cloud sql" while "app engine is recommended for webhosting".
>>
>> I'm assuming this is wrong and and a 3-5x slower query performance to 
>> Cloud SQL from GAE isn't an expectation? Any pointers in terms of where 
>> this may be failing?
>> I haven't yet tried via Public IP and wasn't keen to but I will likely 
>> repeat my tests on both to see if that makes any difference and post my 
>> updates here.
>>
>>

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