I mostly agree, but it's important to note that Paris is a lot smaller than NYC, so comparisons between NYC boroughs (which are each almost as big as the city of Paris) and Paris' surrounding departments are clearly favorable for NYC.

If you compare cities of similar size, i.e. Paris with Los Angeles (which is still bigger, both city and metro area), then the european capital is significantly ahead in density (and I did not cherry pick Los Angeles specifically, it's the same for Chicago, Houston, etc.), and the difference is very significant: Even the core of those US cities (excepting NYC) is less dense than the 3 inner Parisian suburb departments (!!).