DDR3 is not backwards compatible with DDR2.
While both types of modules have similar numbers of pins, the notches in the PCB are in different locations. In other words, a DDR3 module cannot be placed in a DDR2 memory socket, and vice-versa.
DDR3 uses less power.
DDR3 modules run on 1.5V compared to the 1.8V that DDR2 modules require. The DDR3 decrease in voltage results in less power consumption and greater energy-efficiency at comparable speeds.
DDR3 is faster.
From a speed (or frequency) perspective, DDR3 picks up where DDR2 left off. DDR2 "JEDEC standard" memory typically stops at around 800MHz whereas the introductory speeds of DDR3 when it was released in 2007 started at 800MHz. Current DDR3 memory runs up to 1866MHz and performance DDR3 modules (Crucial Ballistix) are capable of running at speeds greater than 2100MHz.