Using 1000 people per square mile (ppsm) as the census tract threshold density for being built up (386/km2), I determined the built up areas for both cities.*
Area: 114.2 sq mi
Standard Density: 11,898 ppsm
Weighted Density: 38,433 ppsm
Urban Area: 277.5 sq mi
Standard Density: 9,900 ppsm
Weighted Density: 30,602 ppsm
The idea behind weighted density is that it describes the density of the average neighbourhood and takes into account that many cities will have large swaths of land with relatively few people living in it. Chris Bradford at AustinContrarian explains this in further detail here and here.
The two cities follow a surprisingly similar density distribution pattern, in future blog posts you'll see that many other cities had rather different patterns. Montreal skews a bit denser though, despite being a newer city. Both cities consist largely of attached 2-4 storey housing on an extensive street grid, although Montreal is more multifamily. Also, while many cities began building neighbourhoods at lower densities in the early 20th century, this was less true for Philadelphia and Montreal. Philadelphia continued building rowhouse neighbourhoods into the early 1950s and Montreal continued building multi family neighbourhoods well into the 1960s.
I'm not sure which one was most working class or most crowded (in terms of living space/capita). Philadelphia is known for being a working class city but Quebec in general was less wealthy than the rest of Canada and the United States at this time.
Of course since Philadelphia was about twice the population of Montreal, the total population living at high densities is greater (except at the very high end).
Comparing to 2010, not only was there an increase in the population of low density neighbourhoods, but it looks like the dense parts of Philadelphia experienced a shift from about 50,000 ppsm to about 20,000 ppsm, and their total population decreased. This is not too surprising considering decreases in household sizes and urban decay in parts of Philadelphia (and Camden).
Montreal also saw a substantial increase in low density neighbourhoods, although these were more around 10,000 ppsm rather than 3,000 ppsm in Philadelphia. Philadelphia also has a lot of people living in exurban areas of less than 1,000 ppsm, close to 1 million (not shown on the graph) compared to about 200,000 for Montreal. The density of Montreal's densest neighbourhoods also decreased substantially, like with Philadelphia, going from about 40-90,000 ppsm to 15-40,000 ppsm. Many neighbourhoods of Montreal, while appearing relatively intact, saw great decreases in population (50% or so), suggesting major reductions in household sizes and crowding.
Unlike for Philadelphia however, the total population living at these "dense core" densities actually increased, suggesting a substantial amount of moderate-high density was built after 1951 either as infill of lower density neighbourhoods or as new neighbourhoods entirely.
Neither city appears to have experienced very high density (ie midrise or highrise) development in sufficiently significant quantities to show up on these graphs.
PS: Density will be a topic in many of my posts, so far I have a fair bit of readers from both Canada and the United States. Do you prefer measuring density per square mile or square kilometer?
*This is relatively consistent with the way urban areas are determined today in both countries. Statistics Canada uses 1036 ppsm (400/km2) as the threshold while the US Census Bureau uses 500 ppsm as the threshold for including fringe areas to the main urban area, however both agencies delineate urban areas at a smaller scale than census tracts. This means that if you have a small satellite town separated from the suburban fringe by 2km of farmland, it wouldn't be included if delineated at a small scale as these two agencies do, but that entire town and farmland might fall within a single census tract which might still be dense enough to be included if urban areas are delineated at the census tract level. Since census tracts are the smallest scale at which data is available for 1950, I'm hoping that 1000 ppsm is a high enough threshold that the result will be comparable to an urban area delineated at a smaller scale with a 500 ppsm threshold.
Also, the 1000ppsm + census tracts have to be contiguous, and enclaves of lower density were included.