I just bought a new 32GB flash drive. I'm using it to copy files from an old to a new computer. Often when inserting it for a new chunk of data it gives a message something like 'this device has errors, scan now to correct' But every time I scan Windows says 'No errors found.' I did this about 3-5 times, with the same result and quit scanning.
You could just remove the HDD's from the computer plug them into the other one and copy it across
If you are on the same LAN connection, you could just copy the files through lan
You could open up a dropbox or google drive account, Sync your data to that so you have a proper backup then sync it on another computer which will download it.
USB seems the slowest of the slow solution to copy files.