Yes, irrespective of the two computers being compared, the one that's not using WiFi connection should have faster download speed than the one which is using WiFi.
It could be poor ethernet cable, or network card either needs a newer driver or the card itself is ready for replacing.
Back on the subject of drivers, it can also work the other way sometimes. A new NIC driver can have adverse affect on network speed compared to previous driver, so it's worth experimenting with a driver roll-back too.