Why perborate is greener bleaching agent?
According to Wikipedia, "Chlorination... can oxidize organic contaminants, producing chloroform and other trihalomethanes, which are carcinogenic, and many hundreds of [other]... by-products.

[W]hen household bleach and wastewater were mixed, 1–2% of the available chlorine was observed to form [halogenated] organic compounds."

Perborates, percarbonates and similar bleaching agents, while strong oxidizers, will not create these chlorocarbon chemicals (unless the chlorine is also supplied). 

However, boron and perborates are not entirely "green". Boron compounds are somewhat toxic. If the prices were the same, I'd prefer percarbonate bleach to perborate.