PeerIndex is calculating influence by an own ranking algorithm described here. The service is taking online acitivities into account as well as connections. By claiming a profile PeerIndex enables to improve accuracy of gathered data. To get some additional information about the service, here is an article by Technology Review about PeerIndex.
The approach of Empire Avenue is rather entertaining than relying on a scientific scoring system. The service aims to enable people to make relevant connections and to discover new services. Furthermore the service provides a fantasy stock market to trade shares about companies in general and to showcase members by associating virtual shares to their authority. These virtual shares may become the basis to get rewarded by companies and to get into business. Below is an introductory video about Empire Avenue.