In our experience, Z-Wave has been the preferred device network. Z-Wave does not require internet for device communication, but does require a hub and a control system, such as HomeSeer, Alexa or Google Home.
WiFi usually requires an internet connection to the "cloud" to interpret device commands and status messages. The advantage to WiFi is ease of setup and number of currently manufactured and supported smart devices. WiFi does require a robust router to allow for the number of devices that might be connected to your system.