This isn’t an either/or situation. The two can co-exist and enhance each other. You can use a Powerline network to extend your Ethernet, your Wi-Fi, or both. (I’m assuming you already have a router with both Ethernet and Wi-Fi.)
Powerline technology turns your home’s electrical wiring into a network. The HomePlug Powerline Alliance provides standardization over products from different companies.
You need at least two Homeplug adapters for a Powerline network. You connect one to your router via Ethernet, and plug it into an AC wall socket. You plug the other into a wall socket in a room too far away for a good Wi-Fi signal, and it gives you one or more additional Ethernet ports. These act as if they’re directly plugged into your router–even if they’re on the other side of the house. You can usually buy these two adapters together as part of one “starter kit.”
When I first set up my own Homeplug system, I was truly astonished by how easy it was. For once, the overhyped expression plug-and-play seemed appropriate.
Using Powerline to extend your Wi-Fi network takes a little more work. You’ll need a HomePlug Wi-Fi adapter, which is basically a regular HomePlug adapter with antennas. But you’ll also need to set up this adapter with an SSID (translation: a network name) and a password. To effectively extend your existing Wi-Fi network, simply give the adapter the same SSID and password as your existing Wi-Fi network. Your adapter should come with instructions on how to do this.
Although I’ve had mostly positive Powerline experiences, the technology has its problems. For instance, you can’t plug an adapter into a surge protector–unless you buy a HomePlug-compatible surge protector. Other problems can be more serious. Logitech offers a useful list of known Powerline problems here.