When comparing the nutritional profiles of all three, they pretty much have identical amounts of calories, fats, carbs, and protein per serving. But pistachios are much higher in potassium (310mgs) compared to almonds (210mgs) and peanuts (180mgs).
Beyond the label
To see the real nutritional value of pistachios, we have to look beyond what's on the label. Pistachios are high in phytosterols. Phytosterols help fight bad cholesterol and remove it from the body, all while having no effect on your good HDL cholesterol. Pistachios are also an excellent source of Vitamin B6, copper and manganese. More importantly, pistachios are high in something else...antioxidants! The USDA compared over 100 different foods and classified pistachios in the group with the highest antioxidant capacity. Antioxidants are extremely important because they help fight free radicals in our bodies.
Conclusion:
Get to crackin'! I've found pistachios to be a wonderful (yeah I said it) addition to my diet. They taste great and are fun to eat. Make sure to get the unsalted kind and never buy them unshelled. Cracking them prolongs the eating process allowing you to reduce your caloric intake without restricting your calorie intake, a process known as the "pistachio principle".