I don't know of any software that detects renames/moves across a whole folder hierarchy. That would be fairly slow, as it would have to scan all files to compare them.
The feature was once proposed as a patch for rsync (google for "rsync detect-renamed"), but apparently it was never accepted into rsync.
rsync does have a limited version of what you are looking for:
This option tells rsync that it should look for a basis file for any destination file that is missing. The current algorithm looks in the same directory as the destination file for either a file that has an identical size and modified-time, or a similarly-named file. If found, rsync uses the fuzzy basis file to try to speed up the transfer.
This will not work if you move files between directories, though.
That said, most sync programs do have the option to remove files in the destination if they are missing from the source, so a move should be replicated as new+delete, which requires more copying, but would work.
If you just want to compare drives, not sync them, you could just write a small script that lists all files with their filenames (and maybe a checksum), and import that into a spreadsheet or small db. Then you can sort by filename or checksum, and directly compare the lists of files. That might be the easiest route.