Most of the differences will stem from the fact that F# is descended from ML while clojure is descended from lisp.
So F# has a more ML/OCaml/Haskell feel with emphasis on:
- static typing
- type inference
- pattern matching
While clojure has more of a Lisp feel with emphasis on:
- s-expressions
- macros
- closures
Also as Brian noted, F# is a .Net language while clojure is a JVM language so each will have access to a vast but different set of libraries.