What kind of wine holds better after it's opened, white or red?
Generally speaking, red will last longer. Red wine contains tannins, dusty compounds derived from skins and seeds that help shield juice from oxygen. Contact with air eventually kills the wine, robbing it of fruity flavour and imparting a cooked or bruised quality. Unlike reds, the vast majority of whites are separated from skins prior to fermentation, so their tannin content is negligible.
Flavour loss depends on the wine style, though. Lighter reds, such as gamay and pinot noir, tend to contain lower tannin levels, so they spoil faster than fuller-bodied reds, such as cabernet sauvignon and merlot.
There are other variables. Cold curbs the pace of spoilage. So if you're in the habit of storing opened whites in the fridge and reds on the counter – the common practices – you may notice that your whites survive better than, say, gamay or pinot noir but perhaps not as well as cabernet. I'd suggest the fridge no matter which colour. You can always let reds warm up on the counter for an hour prior to serving. Either way, a half-finished bottle will lose its vigour and freshness considerably after about two or three days.
Should you wish to extend the shelf life even longer, try the freezer. It won't harm the wine, at least not much. Just be sure the fill level has been reduced by at least a couple of ounces. Liquids expand when frozen. That's why an unopened bottle will shatter or push up the cork in the freezer.