I would say that, on average, a nomadic society would have a lower population density. After all, by definition, they wander about (well, perhaps "wander" isn't the best term). The point, though, is that nomads take advantage of natural resources - open land, for instance. For example, Mongolian nomads used open land to graze their horses. Plains Indians (if you'll pardon the phrase) often followed herds of buffalo. But when the buffalo weren't there, they weren't there. And when the grass in a certain region wasn't good, the Mongolia herders weren't there.
In a "settled-down" society, however, things would be different. People would take all the land they could get, for farming. Also, cities would spring up - greatly increasing the population density. You wouldn't see cities in nomadic societies!