32 bit & 64 bit optimization?

Question: How can I make programs that run better for different operating systems? (64bit and 32 bit)

I know that 64 bit programs are supposed to be faster on a 64 bit operating system than on a 32 bit...
I'm using WXDev C++ which is basically the same as Dev C++.

Possible Rumor: I've heard from some people that to make a program run faster you must compile it on the machine that you wish to use it on.

Qeustion based on Rumor: So would I have to have a 64 bit Operating system to create a 64 bit program? Or is the Rumor false?
There's more to hardware these days than word size.

You can't really be sure until you run and time it. Looking at the generated assembler might help you get a feel for it.
False rumor. The compiler may run faster if it is a 64-bit compiler, but the generated code should be the same - as long as you tell your compiler the same things on each computer you use it on.
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