Sorry, but I must disagree.
Either x32 or x64 versions of CCleaner will do exactly the same job for x32 applications ONLY.
If you want to also clean x64 bit applications you must use the x64 bit version of CCleaner,
otherwise some junk may be omitted - and very probably the x32 CCleaner will not even detect the applications,
because x32 software is NOT aware of the genuine system32 folder - instead Windows will only show it the contents of SysWOW64.
I have not tried an installed CCleaner - I only use the Portable version.
My experience last year with the portable was that when launching x32 I did find it ran x64;
UNLESS I had excluded or renamed the CCleaner64.exe to something else, and then it ran x32 and Analyse found significantly less to clean than x64.
Using Portable, If you unzip the x32 only, you will not get the greater cleaning of x64.
If you Install CC you probably get both and whatever you launch may actually run x64 - if all goes well.
Please note that I am one of very many that use Firefox and NOT Internet Explorer,
and we all suffer from Internet Explorer Temporary files which are created by many applications,
both Microsoft and third party applications.
It is quite possible that these may be x64 bit applications, and perhaps they will create 64 bit junk even though 32 bit IE9 does not
and if you succeed in using x32 CCleaner a lot of this 64 bit junk will never be removed.