The problem with comparing root beer to ginger beer and birch beer is that the former is most often a super-cheap, mass-market, corporate food item, meaning it's made with high-fructose corn syrup and artificial flavorings. Whereas the latter are usually more gourmet-type items, sweetened with cane sugar or fruit juice, and using natural flavors.
There is a really good brand of root beer made with cane sugar that's not ridiculously expensive -- it's called Bergdorf's or Bergman's or something like that. If you live in Texas, they have it at H.E.B.