When I last benchmarked Redis vs. PostgreSQL for a simple k/v cache it was about ~1ms for PostgreSQL to fetch a key, and ~0.5ms for Redis with a similar setup as in this post (although I used "value bytea" instead of "value string" – I don't know if it matters, probably not; 1ms was fast enough that I didn't care to test). I didn't measure setting keys or req/sec because for my use case keys were updated infrequently…
A difference of 0.5ms is negligible with single digit network latency. You would need significant batching to experience the effects of this difference. Of course such sensitive environments are easily imaginable but I wonder why you'd select either in that case.
Yes, that was my take-away.