Benchmarking is hard. And expensive. And in the installations most of them are done, SQLite won't even be tested, because it's designed for completely different workloads and simply doesn't deal with the situation. (For example, any real benchmark will have clients running on different machines from the server, which SQLite AFAIK doesn't really do - whereas it does do very well in the case where you have a single client locally).
You can always look at something like spec, for example http://www.spec.org/jAppServer2004/results/jAppServer2004.html that shows both pg and mysql at least. But beware that the hardware platforms are different (and that these tests are also not from today).
But the bottom line is that if you want to compare performance for your application, the only really relevant benchmark you can run is your own application in a testing environment.