What is an old city ? to begin with, an area in which the layout and the parcels are older; buildings are renovated and change much faster than usually thought, and but for some exceptions even the most medieval cities have a substantial share of their buildings with less than 200 years. Usually they are places with smaller parcels, as the technical and financial tools used to build housing were much more limited in precedent centuries.
You can note that the “grain” (relation of size among parcels) of historic Madrid and of San Telmo, the historic core of Buenos Aires, is similar. The layout is strictly different, as Madrid has a more organic system on which trials of a more regular city have been disposed, as the Plaza Mayor, built from 1576 (nearly the time of the second foundation of Buenos Aires).
Central Madrid has more ceremonial spaces than central Buenos Aires; the argentine capital compensates with an overwhelming array of wide boulevards (as the Avenida de Mayo, linking the hughe dome of the Congress to the Casa Rosada) and is position near the Rio de la Plata (which unfortunately cannot be seen from the urban core).