Although there are some details about what kind of pushdown are supported by the FDWs (for example: to do a WHERE key=x, a non-toy Redis FDW should push the equality predicate to redis), it's no faster nor slower than calling a C function a bunch of times.
Because SQL execution in Postgres (and most other systems) has an advantage of being functional, most executors can save a lot of time avoiding garbage collection and reference management if one is to compare them to, say, Ruby. It's probably going to be faster than bouncing to redis in your application and then to Postgres, for reasons of network overhead.
So, all in all, "it depends", but it should not be slow for a good-quality FDW that pushes down operators well.
Because SQL execution in Postgres (and most other systems) has an advantage of being functional, most executors can save a lot of time avoiding garbage collection and reference management if one is to compare them to, say, Ruby. It's probably going to be faster than bouncing to redis in your application and then to Postgres, for reasons of network overhead.
So, all in all, "it depends", but it should not be slow for a good-quality FDW that pushes down operators well.