The 9800GT green edition is a heavily toned down and underclocked 9800GT. It doesn't require any PCIe connectors since it doesn't need them. Your motherboard will provide enough juice.
The 9800GT GE performs about 20% weaker than the standard 9800GT, or about roughly equal to a 9600GT.
The 8800GTX is a power hungry card card based on energy inefficient older architechture, and consumes far more power than 9800GT, 9800GT GE, and even the 9800GTX. If your PSU could run a 8800GTX, it would have no problems running anything up to a 9800GTX.
Nonetheless, your Zalman 600w PSU is a very good quality PSU, and you can easily run any single GPU card in existence, or even some dual-GPU configurations.