Akka.FSharp is an idiomatic Akka.NET API for F# that defines actors and changing actor state using F# functions. It has been downloaded more commits and commits in recent years compared to Akkling, another F# Akka.NET library. Both libraries support features like defining actors, persistence, and clustering, but Akkling has additional features like lifecycle events, distributed data, and Akka Streams integration. The presentation provides examples of using Akka.FSharp and Akkling for actor programming in F#.