The brewing process turns sugar to alcohol. With some 'continental' lagers (particularly Pilsners) hardly any sugar is left, which is why such beers are popular with diabetics.
However there's a fair bit of sugar left in most beers, which is generally substantially more than there is in red wine. That, of course, assumes that you're sticking to grapes like Cabernet Sauvignon. If you drink sweeter red wines, such as some of those from Greece or Cyprus, you'll still find quite a bit of sugar. (Similarly Beaulolais Nouveau contains quite a bit of sugar. That's both because it's made from the naturally sweet Gamay grape variety and because the quick way that it's made doesn't give time for all of the sugar in the grapes to be turned to alcohol).
Chris