There are special cables for connecting two computers together (which are not the USB3 cables). If you are using your USB3 cable, you have to copy from one computer via the cable onto a memory stick or external hard drive. Then you have to plug into the other computer with the cable and copy the files from your external drive onto the hard drive of the computer. To take full advantage of USB3 you need all devices you are using to be USB3. All versions are backward compatible but data transfer is only as fast as the slowest version. E.G. USB3 hard drive - -USB2 memory stick = USB2 transfer speed. USB3 hard drive - - USB3 memory stick = USB3 transfer speed.
Thanks for the vote. Hope you don't spend too long transferring your files over. May I suggest you keep a copy of the files on your external memory/drive for safe keeping, or even burning them on a disc (that is if you have not done so already)