Finding two spaces that can be compared directly in two different and distant cities is far from easy. This is quite clear for the sites of political power; I don’t know how the spaces around the 50 state capitols in the USA are, but I am sure that even when many of the buildings seem almost identical on photos, their urban position is different (wikipedia even says that 7 of them even have no dome…).
In Buenos Aires and Madrid, lets take two relevant spaces: Plaza de Mayo in the Argentine capital, Plaza de Oriente in the Iberian city.
The Plaza de Oriente is a space designed during the short reign of José I Bonaparte, creating an urban space subordinated to the Palacio Real, by Sabatini, a magnificent building. The architectures and the layout of the square are uniforme, but they do not reach the qualities of the palace. The Teatro Real is also a historical building with values, but again not reaching the level of the palace. Besides, the trees give a good visual barrrier, broken by calle Bailén to favor the Palacio Real, giving good views towards the surrounding areas. The differences of level are good for that.
The Plaza de mayo is an evolution of the Plaza Mayor designed in 1580 by Juan de Garay, founder of Buenos Aires, as a 100×100 m rectangle. What now is the Casa Rosada (the residence of the President of the Republic) was already the center of power in these first colonial times. The square evolved over time, becoming a park in the XIXth century. The Casa Rosada appeared as transformation of the original fort on Avenida Ribadavia, and the Casa de Correos appeared at its side in 1853. In 1886 architect Tamburini reunites both buildings in an eclectic compound, and since then there have been many alterations. The Metropolitan Cathedral, to the west, has a magnificent neoclasic façade with a large pediment, solving its integration in the square with a lateral smaller open space as to appear as an independent classical temple; the project dates from 1745, having been finished in 1836. Its current presence in the square is nearly as relevant as that of the Casa Rosada