The “Why ZigBee” question has always had an implied, but never quite worded follower phrase “…when there is Bluetooth”. A comparative study of the two can be found in ZigBee: 'Wireless Control That Simply Works' .
The bandwidth of Bluetooth is 1 Mbps, ZigBee's is one-fourth of this value. The strength of Bluetooth lies in its ability to allow interoperability and replacement of cables, ZigBee's, of course, is low costs and long battery life.
In terms of protocol stack size, ZigBee's 32 KB is about one-third of the stack size necessary in other wireless technologies (for limited capability end devices, the stack size is as low as 4 KB).
Most important in any meaningful comparison are the diverse application areas of all the different wireless technologies. Bluetooth is meant for such target areas as wireless USB's, handsets and headsets, whereas ZigBee is meant to cater to the sensors and remote controls market and other battery operated products.
In a gist, it may be said that they are neither complementary standards nor competitors, but just essential standards for different targeted applications. The earlier Bluetooth targets interfaces between PDA and other device (mobile phone / printer etc) and cordless audio applications.
The IEEE 802.15.4–based ZigBee is designed for remote controls and sensors, which are very many in number, but need only small data packets and, mainly, extremely low power consumption for (long) life. Therefore they are naturally different in their approach to their respective application arenas.