Samara Lynn at PC Mag wrote:
The most significant difference between traditional ad-hoc wireless networking (traditional peer-to-peer networking) and Wi-Fi Direct is security. In Windows ad-hoc networks, the highest level of security supported is WEP. Wi-Fi Direct, as mentioned, supports WPA2. Another difference, Wi-Fi Direct devices can also simultaneously connect to existing wireless networks. More granular control and better discovery of devices also differentiate Wi-Fi Direct from ad-hoc networking.
http://www.pcmag.com/article2/0,2817,2371413,00.asp