Complementary technical white papers from Microsemi and the Ethernet Alliance describe the two technologies and explain how they're related.
A recent white paper from Microsemi succinctly explains the differences between the company's proprietary Energy Efficient Power over Ethernet (EEPoE) technology, which takes a multi-pronged approach to reducing power losses throughout PoE power chain elements, versus Energy Efficient Ethernet (EEE) technology, as specified per the IEEE 802.3az-2010 standard.
Separately, a white paper recently produced by the Ethernet Alliance describes the benefits of employing EEE as specified in IEEE802.3az-2010 and EEPoE as allowed by the IEEE802.3at-2009 standard to reduce the energy consumption of PoE switches. The Ethernet Alliance estimates that total energy savings from the combination of EEE and EEPoE technologies approaches 3.13W per link.