I would expect Postgres to be faster for complex operations over large datasets (of course with a helping of "It depends!"), but very interested in knowing if this is generally untrue.
This is generally untrue, depending on what you mean by "faster".
The way most web apps use DBs, sqlite is incredibly fast. Because most web apps make multiple queries, often sequentially, and they're very sensitive to DB latency. The network overhead adds up: https://twitter.com/benbjohnson/status/1514969870529560580