Well, here's the main difference between the 32 and 64-bit AE CS6:
The 32-bit version AE CS6 is a figment of your imagination. It doesn't exist. I repeat: beginning with AE CS5, Adobe never, EVER again made 32-bit versions of AE. Anyone who tells you differently tells you lies.
I'd say that's a pretty clear-cut difference, n'est-ce pas?
As Dave says, After Effects CS5 and later are 64-bit applications. There are no 32-bit versions.