You can support both. You should take look at Typed Racket, Racket w/ Contracts, Erlang Dialyzer, and Qi/Shen. Frankly the Lisp contingent is way ahead on this kind of thinking (would of course love to hear about others).
I'm interested in developing such systems for Clojure and have actively researching something considerably more powerful than Chambers/Chen predicate dispatch.
Qi/Shen is a fusion of Haskell and Lisp, heavily inspired by Haskell. The Lisp contingent is not 'way ahead': they are simply assimilating useful bits of their strongly typed functional cousin languages.
I'm interested in developing such systems for Clojure and have actively researching something considerably more powerful than Chambers/Chen predicate dispatch.