Does Wi-Max wipesout Wi-Fi?

They are different markets. Wi-Max is intended for larger areas, and they are public networks, rather than private ones. Basically, they are nice for roaming around town, but you wouldn't want to have any shares set as anyone on the network could then access your data. Many cities are in the process of setting up such networks for the convenience of their citizens, at little cost to each. Some states (mine included) are considering legislation to protect the service providers from government competition, limiting the cities to installing the networks, and requiring that they be operated by private companies, much like cable systems.