In 1860, the USA was already a significant industrial power. Their population was 31.4 million, and 8.2 million in Mexico. But the US territory was much larger than the territory of Mexico. Also, the majority (2/3) of the Mexican population focuses on the central part of the country (the area surrounded by a red line):
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This area has always been more densely populated than any part of the USA.
the image you give is from the late Twenty century, this one is from 1900 Mexico (source)
this one from USA 1860
Look the more densely populate regions are the one that historically were industrialized, SURPRISE!!!
and The regions USA was more densely populates in the 1850-1860 than Mexico in the 1900 are the one that are the source of that country industrial power. basically new England and the northern territories