I never said that. The memory for the instructions is double.
A 64-bit word is double that of 32-bit and whether or not you're using all the bits, that memory space is still allocated.
I tried x64 Win 7 on an early Core 2 Duo with 1GB of RAM, and the performance was pretty bad. x86 was better since more memory was freed.
However, the memory USAGE of the application itself is not double - and what was the hardware in question? (One thing that has to be taken into account is badly-written or piggy drivers - while not as large an issue as it used to be, it's still an issue, especially for lower-tier hardware and peripherals.) Given identical loadouts, what's the memory usage comparison between Firefox, PaleMoon x64, and Waterfox? One reason I prefer IntelliPoint Pro (and now the Microsoft Keyboard and Mouse Center driver for Windows 8) to SetPoint for my Logitech V220 is due to SetPoint's piggishness - a porky driver that is less usable compared to an alternative gets replaced by that alternative without a quibble. Love the V220 as a wireless mouse physically, but I loathe the porkiness of SetPoint.