Most of us (urbanists?) agree that a few things are needed to improve American cities. First, increased government investment in public transit, as opposed to highways. Second, decrease subsidies for oil and gas. Third, increased planning at the regional, as opposed to local, level.
I think we also all agree on what we want our final cities to look like. First, more walkable/bikeable/busable. Second, less sprawling. Third, mixed-use areas that are affordable for poorer families.
There seems to be a mostly be a disagreement around what, if any, government measures should be used to achieve this end. The Yglesias/Avent argument seems to mostly focus on removing zoning laws that prevent density in cities like DC, Portland, San Francisco and New York, while New Urbanists look to how central planing of cities can prevent the sprawl seen in the sun belt.
Each city is different in the way it has developed but I think Portland is a good example a certain type of American city ideal. In the 1970s the Oregon passed a law mandating that metropolitan areas establish an urban growth boundary. This was mostly done for environmental conservation as opposed to urbanist purposes. As a result, Portland established an urban growth boundary and a regional planning committee. The urban growth boundary establishes a boundary to the city. Any area outside of the boundary is zoned in a way to only allows very low density housing. The low density limits effectively make it unaffordable for developers to build suburbs outside of the boundary. The area is essentially limited to agricultural purposes.
The regional planning committee also began zoning the city in a way that forced office buildings and commercial centers into the downtown of the city. As a result a high percentage of people in Portland work in the downtown core. This is different from other American cities where a lot of the jobs began moving to cheaper land in the suburbs.
By limiting residential growth outwards and forcing jobs into the center of the city it became very easy for Portland to start building effective public transit. If most people are traveling to a single job center it is easier to get them there via public transit because you just need to build a number of light rail main lines in each direction that take people to the center of the city. It is much more difficult to do this in cities where a lot of commuters go from suburb to suburb. Portland also began building mixed-use residential areas along different light rail stops, to encourage the use of light rail. Portland has also limited its development in a way to create walkable and bikeable neighborhoods.
For a certain type of urbanist Portland is an ideal city. It has low sprawl, moderate density, less congestion, great public transit, walkable, bikeable moderate to low congestion etc.
The problem with Portland is that it is extremely expensive. The urban growth boundary has made land a limited resource and the strict zoning laws have made rents in both housing and office buildings very pricey.
On the other hand you have cities like Houston, Dallas, Phoenix and Atlanta. These cities have very few zoning regulations and don't have regional planning committees with zoning authority. As a result you get middle class residents moving to the suburbs and jobs following them to office parks in first ring suburbs. Then middle class residents move out of the first ring suburbs to the second ring suburbs and jobs follow them there to even cheaper office parks, with local city governments offering incentives to move. This results in a decentralization that makes public transit impractical and leads to a downward spiral of sprawl, decentralization and more automobile based transit investment.
However, what you do have in these cities is very cheap housing, as land is readily available. A lot of the times you have a stark segregation between the rich and poor neighborhoods which is a problem. But, unlike Portland and San Francisco, poor people can actually afford to buy homes and rent there.
One of the contentions of Peter Calthorpe, one of the principal New Urbanists, is that cities that are properly built around New Urbanist principles; central planning, reduced sprawl, dense, walkable, mix-used zoning, transit-oriented development, human scale, would be cheap and affordable.
One of the contentions of the Avent/Yglesias/Neoliberal crowd has been that reduced zoning measures would lead the free market to build cities that were more dense and less sprawled.
There are certainly intervening variables at play but I think it is important to note that at this point neither of these contentions has borne out in practice.