It should run fine. I sometimes compile an exe on my 64bit Vista machine and run it on my 32bit XP laptop.
The only thing I can think of is that one of your machines has a security setting that's preventing the exe from running. I'm not familiar with Windows 7 but on Vista I needed to change a security setting - something to do with Data Execution Prevention (DEP) if I recall correctly. Can't recall off-hand where that setting is - and have no idea where to find the comparable thing on Windows 7

. Perhaps someone else can help?