The advantage of ethernet is that you can keep the drive connected 24/7 to your home network. That is great for:
1) Use by more than one computer if you have more than one
2) If you have a laptop, then the disk is available whenever you are connected to your home network (no wires required)
3) If you have a laptop... you can use automatic backups without remembering to connect your drive. When you are not home... backups will be automatically suspended.
If you have a router with a USB connection that supports the addition of HDDs via USB... then you can also use that capability to have a plain USB drive connected and available on your network. Some people have reported some issues with Time Machine... but I do not have direct experience (I use a TC).
/Jim