So it's no surprise that the Redis solution is faster. Besides parsing and indexing the data, PostgreSQL will also prioritize reliability and won't confirm your transaction until it's actually persisted to disk. Whereas Redis is prioritizing speed, and working straight to RAM--the disk serialization is an asynchronous process. If anything, I'm surprised that the Redis solution is _only_ 16-20x faster than PostgreSQL given what appears to be happening.
So, for this use case--storing a cache of Amazon API results for mostly-static data--the Redis solution is a no-brainer: durability of the data is not a serious concern; there's no real risk of data corruption because there's only one schema and no interrelations; you don't need the data store to know anything about the data; you don't need indexing beyond straight key-value. For other use cases, Redis might be entirely unsuitable because of durability or data integrity reasons, in which case the speed benefits wouldn't even matter.
Now, all that said, in the real world there are lots of other considerations: Are you using either of these databases already for some other purpose in the same app? Which data store is easier to set up? Which is easier to code against? Do you even care how fast it is if the slower speed is 11ms on a single-user system?