I don't think you can use USB for a machine-to-machine clone like you can with FireWire. You could temporarily remove the source drive and put it in a cheap USB enclosure and clone from that. You don't mention what machines you are trying to use, but I recall that some Macs allow a simple ethernet cable to be used between them.
Obviously, you could also get a external drive and backup on the source machine, then use that to either restore or migrate your data to the destination machine. Then you will have a backup drive to faithfully use from now on.