Do 32 bit programs work worse in a 64 bit operating system?

Question

Windows

1) Do 32-bit programs work worse in a 64-bit operating system?
2) Does it happen that a 64-bit program is installed in the "Program files x86" folder? Taking into account the fact that the user did not assign the installation to this folder.
OS: Windows 7

Answer 1

1. Yes. 32 bit programs run in emulation mode so they run slower. Especially on Intel Itanium processors.
2. No one ruled out the mistakes of software developers.