I don't think Teracopy can compare files.

Beyond Compare does, it's a wonderful tool for comparing files, directories, even whole drives, and is darn fast at it. It has a very good (graphical) interface too.

You can use other programs (many are free) to generate hash values of files. Then you can compare the results side by side. This can be done manually or even semi-automatically, using a script.

I sometimes use MultiPar (it's free) to create some redundancy (protection) blocks, to repair files or folders that got broken/corrupted.

If you have set Teracopy to verify upon moving and copying, original and copy should be identical. You can automatically save the checksums for re-verification later on.

Transferring (moving) or copying?

It's better to copy, so you retain your original as a "backup," in case something goes wrong at some later time. Then you can always re-check integrity in the future.

I use Beyond Compare on whole drives/volumes to compare/verify integrity and re-synchronize/update from time to time.