The ACR plug-in files for PS-CS6 and PS-CC are in different folders, but the camera profiles and lens profiles are in a common folder. Since updates to ACR are typically handled by the product, itself, not direct-link downloads that you must have saved for ACR 7.1, I don’t know what the error means in relation to CC having a newer ACR.
What version of ACR did you have installed for CS6 before you tried to update to ACR 7.1? Are you trying to downgrade from a higher version of ACR on CS6?
The first thing I would try is install ACR 8.3 RC for PS-CS6, using the CS6-specific link at Adobe Labs.
If you really need to go back to an earlier version of ACR, then the Adobe-approved method is to uninstall PS, entirely, then re-install it to get the older version.
It may be that you have to uninstall both CS6 and CC and then install CS6, first, and get it updated the way you want it, then install CC, again, and update it how you want it. That seems like a lot of work, though.
Why are you wanting to install ACR 7.1 for CS6?
If you plan ahead, then the way you can switch between different versions of the ACR plug-in, is to save your Camera Raw.8bi file each time you upgrade (I rename mine so the extension is the version: Camera Raw_8bi.71 and leave them in the same folder), and just replace whatever version of the ACR plug-in with that one you want.
As per your post you are already having 8.3 ACR CS6 on your system, so when you are trying to install 7.1 which is an older version it fails.
To install 7.1, you need to re-install PS CS6 to have ACR 7.0 first.
Or you can wait for 8.3 live release.
Thanks Ashutosh - That was my thinking, but glad to get confirmation. I did install the lastest beta of ACR (8.3) which does now include the chromatic abberation (most important to me), but still is not able to erase using the adjustment brush. At this point, I'm just going to wait for the live release.
That said, do you have any idea when it might be released?