What's the difference between green vs. white grapes? Absolutely nothing, those are two names for the same thing. Somewhat similar to an albino animal, recent research suggests that the only reason we have green grapes is due to a gene mutation in the plants history. In other words, they are biological similar to black and red grapes but lack a regulatory gene (VvMYBA1) which is responsible for the production of anthocyanin - the dark pigment responsible for their color (1).
Because of their milder taste, people tend to prefer the white variety when it comes to snacking and as an ingredient for recipes. That's too bad, because with that choice they are missing out on powerful antioxidants. There is a significant nutritional difference between red and green grapes. From what you see reported on the nutrition label, you would conclude they are the same but that only tells half the story. Per a 3.5 ounce (100 gram) serving, it is true that both varieties have 69 calories, 18 grams of carbs, 0.72 grams of protein, and comparable essential amounts of vitamins C, E, K, A (in the form of beta carotene) and minerals like magnesium, iron, copper, and calcium.
However when you look at the ORAC values for each, the difference is clear. The amount of antioxidants in white grapes vs. red grapes is significant; 1018 vs. 1837. This means you are getting almost half the antioxidants with green as you are with the red version. The reason for this is that missing pigment discussed above. Those anthocyanins are type of flavonoid which is a powerful antioxidant.
You're also losing out on resveratrol with white grapes. How much? Well if you take the average serving size for a glass of wine (150 ml), you will find 0.01 to 0.27 mg of resveratrol in white wine versus 0.30 to 1.07 in red wine (2). The specific white wine that tested for having the highest concentration of resveratrol still had less than the lowest tested red wine.
As you are probably aware, during the past couple decades a great deal of resveratrol research has been done which suggests the compound may activate the "longevity gene" in humans (3), though further studies are needed in order to conclusively determine that.
So are green grapes healthy? Absolutely. But if you want the healthiest version, go for the red or black varieties.
USDA Database for the Oxygen Radical Absorbance Capacity (ORAC) of Selected Foods, Release 2 - Prepared by Nutrient Data Laboratory, Beltsville Human Nutrition Research Center (BHNRC), Agricultural Research Service (ARS), U.S. Department of Agriculture (USDA) - May 2010