My wi-fi router has two frequencies and protocols - /g and /n I think. It's possible the older computer has only the older protocol and the laptop has the new one.
Certainly a direct connection with wires will have better performance by skipping the transmitting and receiving steps and I would try that to see if that's involved.There may also be interference from other users of wi-fi in the area leaving insufficient bandwidth for everyone to talk at the same time.