. The USDA (United States Department of Agriculture) says that pistachios contain more anti-oxidants than green tea.Pistachios are packed with vitamins, fiber and nutrients, and just adding a handful or two of pistachios to your daily diet can make a big difference in helping reduce the risk of heart disease. They do of course contain fat but almost 90% is the "good" unsaturated fat, and they are also a source of protein.