Do 32 bit apps run slower (on Windows 7) on the 64 bit version than on the 32 bit version?

It will run slightly slower as it has to be run through WoW64 emulation. The difference is probably not significant enough for you to notice, but it is there.

"It's a very contentious and fact-specific issue. There is no one right answer.

No emulation is required for normal code, only on system calls. For most applications, system calls are a miniscule fraction of their resource consumption. So one would expect it to be very, very close to identical in most realistic cases.

If the system has 4GB or more, likely the benefits of the extra memory will outweigh the slight overhead of translating on system calls. 32-bit Windows 7 is limited to about 3.5GB. The extra memory forms a larger disk cache, and disk I/O is more expensive than almost anything else a typical system does."