Supposing that memory is not an issue does targeting a 64 bit OS make a C/C++ Windows console application run faster?
Update: Prompted by a few comments/answers the application involves statistical algorithms (e.g., linear algebra, random number draws etc).
Replying mostly to the edit, not the original question: I've ported one application that's heavy on statistics and (especially) linear algebra to run as 64-bit code. For that code, the effort was minimal, and we got about a 3:1 improvement in speed.
I suspect that the majority of the notion that there often won't be comes (usually indirectly) from companies who have code that won't be easy to port, and are doing their best to tell customers why it's a good idea to continue buying their program, even though it's still 32-bit code. Of the code I've ported (or just "recompiled" in most cases) none has come out any slower as 64-bit code, and most has come out at least a little faster.