I am curious as to how F# performance compares to C++ performance? I asked a similar question with regards to Java, and the impression I got was that Java is not suitable f
I don't think that you'll find a lot of reliable information, unfortunately. F# is still a very new language, so even if it were ideally suited for performance heavy workloads there still wouldn't be that many people with significant experience to report on. Furthermore, performance is very hard to accurately gauge and microbenchmarks are hard to generalize. Even within C++, you can see dramatic differences between compilers - are you wondering whether F# is competitive with any C++ compiler, or with the hypothetical "best possible" C++ executable?
As to specific benchmarks against C++, here are some possibly relevant links: O'Caml vs. F#: QR decomposition; F# vs Unmanaged C++ for parallel numerics. Note that as an author of F#-related material and as the vendor of F# tools, the writer has a vested interest in F#'s success, so take these claims with a grain of salt.
I think it's safe to say that there will be some applications where F# is competitive on execution time and likely some others where it isn't. F# will probably require more memory in most cases. Of course the ultimate performance will also be highly dependent on the skill of the programmer - I think F# will almost certainly be a more productive language to program in for a moderately competent programmer. Furthermore, I think that at the moment, the CLR on Windows performs better than Mono on most OSes for most tasks, which may also affect your decisions. Of course, since F# is probably easier to parallelize than C++, it will also depend on the type of hardware you're planning to run on.
Ultimately, I think that the only way to really answer this question is to write F# and C++ code representative of the type of calculations that you want to perform and compare them.