First off, 32-bit or 64-bit indeed makes no difference from a filesystem point of view.
However, I respectfully disagree with carwiz in that the harddisk must be connected via SATA, any SATA-to-USB adapter will do the trick.
What isn't clear is which of your two drives you intend to perform data recovery on, and which one you reinstalled your OS on. Are we talking about both of your drives or just one?
If the data you seek to restore is on your other drive (not the C: one which you reinstalled) then you can just go ahead and run the recovery software right from C: - no need to fuss with using a different PC and moving drives and all that.
BTW, might I also recommend Recuva from Piriform which is small, fast, and really works well.