Do you mean local USB vs network Ethernet?
If so the obvious advantage is at Ethernet puts the printer onto the network for all users to print to directly. I have a wifi printer on my network and it works great.
If you mean connecting either USB or Ethernet to a router with both ports, for example, then it's down to the speed - Ethernet will get data to the printer faster.
If the printer is shared it makes more sense to use Ethernet to connect the printer directly into the network, that way you won't have to use a "host" computer that has to be turned on whenever somebody wants to print something.
If you're the only person who uses the printer, however, then it makes more sense to wire the printer directly into your computer via USB. Assuming you're not on a laptop of course, in which case connecting the printer to a wireless access point via Ethernet would make more sense so you can print wirelessly.
The Ethernet connection can do everything the USB connection can do and more.
It keeps your printer independent and not reliant of your PC being on to print. This will make it easily accessible to other devices if your PC is off. You are not limited to the length of your USB cord (6ft) so you will have more flexibility in where you can place your printer.