Powerline is usually much better. As long as there isn't an issue with the electrical wiring. Performance can be similar to a direct Ethernet connection. Even if not as fast latency is about the same.
WiFi extenders just repeat a signal. You place them about halfway between and they repeat the signal. As a signal will degrade on the way to the extender. It is repeating that degraded signal. Each time it hops an extender. There is a performance impact. Also extenders usually require using a different SSID. Forcing you to manually manage connections on mobile devices.
Powerline adapters also come in WiFi varieties. You get the benefit of a low latency signal over your powerline to the WiFi plug. Rather than repeating your WiFi. It acts as an Access Point. If you give that Access Point the exact same SSID, Network Key and Encryption type as your main router. Your devices will connect automatically to the strongest signal. These WiFi plugs also normally have Ethernet jacks. Allowing you to hardwire a stationary device (PC, TV, Game Console) and connect mobile devices wirelessly.
MoCA adapters are also an option. They use the COAX cables for TV instead of Powerline. As far as I can tell they are just as good but there aren't as many options. They aren't as likely to run into interference. But they can cause issues with some TV providers.
Mesh has much of the same problems as WiFi extenders. As they are repeating signals. They just cost a lot more and allow all mesh devices to use the same SSID. Something Apple's Airport did a long time ago.
My order of preference for mixed Wifi/Hardwire networks would be
- Ethernet run to Access Points (or routers set to act as Access Points)
- Powerline (or MoCA) Ethernet Adapters to Powerline WiFi access points or Powerline Ethernet to Powerline Ethernet to Access Point
- Mesh
- Range Extenders
The TP-Link WPA8630 V2 is quite good for WiFi + Powerline. They label it Range Extender but it is an Access Point. Careful on the selections as some are Powerline only.
Amazon.com: TP-Link AV1300 / AC1350 3-Ports Gigabit HomePlug Powerline Wi-Fi Extender Adapter 2-Kit (TL-WPA8630 KIT V2): Computers & Accessories
www.amazon.com