DiCaprio's Gangs of New York came out in 2002. It covered the 1840s/50s/60s. https://en.wikipedia.org/wiki/Gangs_of_New_York

I do not think I could distinguish any difference in the NYC of the 1850's vs 1910's (before cars were popularized). Electricity was available for the first time in 1890, but the first application was textile mills. The first skyscraper was 11 stories in 1890? I don't think 1 person in a thousand could distinguish those time periods.

Without getting into it too much, I think folks could. The gilded age (1870s-1890s, give or take) produced a lot of buildings of a different style, and comparing 1850 to 1910 could be clear. Easier still are subways. They might not have been at their fullest extent in the 1910s, but they were quite present beforehand, and nonexistent in the 1850s. But the biggest that your average person could pick out would be Central Park: built in the 1850s, not finished until later.