PS CS 6 on 64 bit machnie offers you both the options 32 bit as well as 64 bit.
Its your choice to install both or any one of it.
64 bit Photoshop can utilize more RAM installed on your machine and will respond better to larger files as compared to 32 bit
On 32 bit OS , there is no choice given because the only option left out is 32 bit photoshop.
If you install both the versions, there will be "NO PROBLEM AT ALL"
Is there a reason to install BOTH?
Yes. TWAIN for scanner support and other legacy support features that only exist as 32bit software.
Thanks for both responses. Makes sense and now I get why I'd want both versions and not just the 64bit.
Moving this discussion to the Photoshop General Discussion forum.