A major difference, which is probably a result ofthe purity but I less see mentioned, is the pervasive use of monads. As is frequently pointed out, monads can be built in most any language, but life changes greatly when they are used pervasively throughout the libraries, and you use them yourself.
Monads provide something seen in a much more limited way in other languages: abstraction of flow control. They're incredibly useful and elegant ways of doing all sorts of things, and a year of Haskell has entirely changed the way I program, in the same way that moving from imperative to OO programming many years ago changed it, or, much later, using higher-order functions did.
Unfortunately, there's no way in a space like this to provide enough understanding to let you see what the difference is. In fact, no amount of writing will do it; you simply have to spend enough time learning and writing code to gain a real understanding.
As well, F# sometimes may become slightly less functional or more awkward (from the functional programming point of view) when you interface with the .NET platform/libraries, as the libraries were obviously designed from an OO point of view.
So you might consider your decision this way: are you looking to try out one of these languages in order to get a quick, relatively small increment of improvement, or are you willing to put in more time and get less immediate benefit for something bigger in the long term. (Or, at least, if you don't get something bigger, the easy ability to switch to the other quickly?) If the former, F# is your choice, if the latter, Haskell.
A couple of other unrelated points:
Haskell has slightly nicer syntax, which is no suprise, since the designers of Haskell knew ML quite well. However, F#'s 'light' syntax goes a long way toward improving ML syntax, so there's not a huge gap there.
In terms of platforms, F# is of course .NET; how well that will work on Mono I don't know. GHC compiles to machine code with its own runtime, working well under both Windows and Unix, which compares to .NET in the same way, that, say, C++ does. This can be an advantage in some circumstances, especially in terms of speed and lower-level machine access. (I had no problem writing a DDE server in Haskell/GHC, for example; I don't think you could do that in any .NET language, and regardless, MS certainly doesn't want you doing that.)
