I can compare old houses at the edge of a city which cost four times as much to new builds at the far edges of that city's metro area which cost significantly less. The more expensive houses require significantly less infrastructure and cost the government less to support because of their location.
A huge undercurrent in urban planning discourse right now (e.g., Strong Towns), is that if all subsidies and taxes were removed both the poor and rich living closer to the city (or in older, denser suburbs) would have more money at the end of the day, while most living in significantly less dense housing would not be able to afford to pay for their lifestyle.
I'm certain this logic only applies to mega cities. The vast majority of smaller cities and towns are like one or two streets of high density and the rest is suburban or rural. There's not actually anyone in the 'city' to subsidize those around it.
There are a lot of cities in the Rust Belt and Midwest like I described, with the regional population around 1-2 million which are far away from being mega cities.
In the few examples I've personally visited, the residential density in the older "upscale" neighborhoods tends to come from duplexes and single family houses on small lots (or larger lots with a comparatively small amount of street frontage). There's some large buildings mixed in along with some very upscale condos and row houses.
Outside of extreme cases, infrastructure costs tend to become dominated by how long the road or pipes are, rather than the number of people using them.
A huge undercurrent in urban planning discourse right now (e.g., Strong Towns), is that if all subsidies and taxes were removed both the poor and rich living closer to the city (or in older, denser suburbs) would have more money at the end of the day, while most living in significantly less dense housing would not be able to afford to pay for their lifestyle.