Obviously public transit uses less energy. But city dwellers go out much more, whereas rural is more likely to just stay home. Even a basic framing that recognizes telecommuting might not be enough to capture this - if farming and factories are generally not in cities, then having a bunch of people living in cities just to do reverse commutes to less dense areas is going to be worse.
Single family detached dwellings most certainly take more energy to heat. On the other hand if the heat is coming from burning wood, that's renewable in both energy and carbon senses. Modulo particulates of course, but that points to an advantage of lower density.
Urban living also results in much higher rents for housing, with that now-centralized wealth being more likely to be squandered on the upper classes' hedonism landfill.
I'm certainly not rejecting the idea that urban living uses less resources. The hive intuition is quite compelling, and the not-city not-rural hour-plus SUV-commute to a suburban office park lifestyle is clearly terrible. But such comparisons are going to be highly dependent on framing, and those links haven't even done the basics of it.
