I have tried white balsamic vinegar once, and I personally don't really see any use for it. I think it is actually just white wine vinegar with some other type of flavoring added.
Real Balsamic Vinegar is an interesting product. As stated already in a post, any producer can add carmel coloring to red wine vinegar and call it balsamic, but it is not really balsamic. I think that balsamic vinegar, real balsamic vinegar that is, does not fit the definition of what most people think of when they hear the word vinegar. I think that a better way to describe balsamic vinegar would be to call it a syrup, because it is thick and sweet and no where near as acidic as wine vinegar.
As stated by someone already, you can reduce commercial balsamic vinegar from the gallon jugs and it will concentrate the flavor, but it is still just red wine vinegar and carmel color. Real balsamic vinegar is actually made from WHITE trebbiano grapes and aged in different kinds of wood barrels. The aging in the wood barrels is what gives it the dark color, and over time it becomes thick and sweet. If you take a bottle of real balsamic vinegar that is half full and turn it upside down, it should coat the bottle completely like molasses.
I do think that commercial balsamic vinegar is good for salads and things like that, but I think using real balsamic vinegar in a vinagiette would be a waste and WAY too sweet. I think it should just be drizzled on things to finish them.
Real balsamic vinegar is rather expensive, but there is one type which is affordable and comprable to traditional Balsamic vinegar. Someone stated before that a consortium rates the vinegars and gives them a stamp of certification. This balsamic is not certified traditional, but it is as close as you can get without paying the hundered plus dollar price tag that comes with a traditional bottle which is only about two ounces.
It is called VILLA MANODORI. It is about thirty five dollars per 8 ounce bottle, a very good deal considering the alternative traditional balsamic vinegar.