Questions that seem to come up frequently when I am lecturing about wines include “Does it have to be red in order to get the health benefits?” and “Which types of wine have the highest amount of the healthful polyphenols?” To answer the first, red wines do have much higher levels of resveratrol and other beneficial compounds for several reasons. Since these compounds come from the skins and seeds, the whole grape (berry) must be fermented together in order for optimal extraction. White wines are made by pressing out the juice and then fermenting it without contact of the skins and seeds. So yes, it has to be red for the full dose, and it has to be wine not grape juice.
The second question is a bit trickier. There are natural variations among the different varietals of grapes that wine is made from, but the terroir (local conditions) and methods of viticulture probably have more to do with it. To understand why this is the case, consider why grapes make resveratrol and other polyphenols in the skins in the first place: it is for protection against environmental stress. That is of course the reason why they are such potent antioxidants and anti-microbial agents.
One grape that seems to struggle mightily is pinot noir, so pinots are known to have high levels. One Oregon producer of pinot noir wines has petitioned for permission to state resveratrol content in the wines, which the government has resisted because people might start thinking that wine is actually a healthy beverage (it is.) But other reds have healthy polyphenol content too, and there are several studies now comparing the amount of resveratrol in similar wines from different parts of the world and with different traditions of winemaking.
In the end it may not be all that important, since the evidence that resveratrol explains all of the benefits of wine is pretty scant; for one thing, even wines with high resveratrol levels still don’t have much compared to the amounts used in laboratory studies. Other studies point to the combination of all of the compounds in wine working together as the key, including alcohol. So the answer is drink whatever kind of red wine you enjoy, and if you don’t like red maybe you should continue looking for one that you can at least suffer through.