By the time you copy the data to the USB3 drive, disconnect it, move it to the other PC, connect it, and then copy the files a second time, I would say that directly copying over the LAN will be faster and less labor intensive.
USB 3 has higher bandwidth capabilities, but you really won't see much of a difference between the two. The 5 Gb/s theoretical transfer speed of USB 3.0 will be bottlenecked by a standard hard drive read speed, which averages 80 - 110 MB/s unless you using an SSD for an external. I would go with a gigabit connection, roughly same speed, and easier like PhilFrisbie said.
For your 40GB drive, it is about right to have 65MB/s. Nothing you can do about it apart from enabling write cache. If you already had, then that is it.
Things that determine the speed of the HDD include rotation speed (rpm) and platter density (GB/cm2).