There is more professional work being done in Scala, and it makes it more palatable to managers that it runs on the JVM and allows them to leverage some of the existing knowledge of their Java programmers.
In the financial world, however, F# use is on the rise.
I currently work in F# but not in finance, and the lack of mature libraries for common things (like JSON serialization!) makes it a major pain in the behind.
Were I told to select a functional language, "quick!", I would select Clojure when caffeinated, and Javascript (ES7) when not.
FWIW: I subscribe to the notion that dynamic typing with unit testing will get you a correct and working program faster than static typing. In the case of Clojure, you now have clojure.spec, which means you can write conformance criteria as functions and generate tests and test data.
http://games.greggman.com/game/dynamic-typing-static-typing/
[1]: https://www.coursera.org/specializations/scalaIf you're looking for enlightenment, pick up Haskell, maybe OCaml and skip F#.
Short answer: whichever you can get a job in. That's more important than the design differences between them, which are relatively small.
Long answer: I wouldn't use F# because nice as it is you're eventually going to want HKT. Between Scala and Haskell I'd pick based on your learning style - Scala lets you write familiar comfortable code and incrementally adopt functional features, Haskell forces you to dive straight in and do things the Right Way from the start.
Having gone down the Haskell rathole, it's clear to me that the advertising is better than the product. It's complex and difficult to learn and the "less errors because of typing" mantra turns into 'how in the world am I supposed to find my error'. In practice, I very rarely run into errors caused by type problems.
I know nothing about F#, but that's actually my criticism of it. The F# community is small. I occasionally hear about people playing with F#, but even that is rare. (although it could be that I just don't know enough about it and F# and it's community is awesome)
Scala has a reasonably sized community and is being used in production plenty. I personally don't see any benefit beyond the fact that some people like the syntax better than Java and can do less boilerplate (which, if not paying attention could lead to higher resource consumption).
If I were looking for something new, I'd look into Go and Rust. Both have strong followings, a lot of active development to learn from, and strong job markets moving forward (IMO). Or alternatively reverse-expand back into C and start playing with embedded RTOSs - which has the benefit of both being very interesting and an area where senior people could make a significant impact.
... Now, if you really wanted one of the three - I would choose Haskell for learning, Scala for job market, F# if you are already a .net developer.
However, Haskell and OCaml are the more classic functional, static-typed languages, and while Haskell has more job opportunities than OCaml, it is probably the steepest learning curve and highest time commitment of all these languages.