Some places like downtown Dallas are even more empty.
If you go outside in the downtown of most 200k+ cities, on any normal day, you’ll find lots of people there.
On the other hand, the residential suburbs will be dead.
But I’m gonna assume the relaxed zoning in the EU, and the resulting mix of commercial, residential, and offices, often even in the same building, leads to the people having a reason to go downtown.
These leads to a pretty common pattern where just outside of the financial/governmental centers of US cities there exist neighborhoods that are mixes of residential, cafe's, nightlife, "creative businesses" or retail. For instance, the Chicago loop is literally surrounded by such places.
But the lack of activity in a financial district has very little correlation to the density of the city. Manhattan is obviously a walkable and dense place to live but lower manhattan (wall street) can feel down right empty after hours.
I have much less experience in European cities, but my experience in Dublin, Amsterdam and Frankfort are not much different than this.
In Toronto the Financial District doesn't go completely dead, but the 4million square foot underground mall shuts down, and it's just a few ground level businesses that stay open. It's still more lively at night than the typical suburb, but not as bustling as the adjacent neighbourhoods or as the Financial District during the day when there 200,000 office workers there (vs just a few thousand tourists and residents within walking distance at night). From what I heard it's not as dead at night as the Chicago loop.
I only visited cities which don’t really have high-margin businesses, so that’s maybe why I never noticed that.
The St. Louis region, where I live, has nearly 3 million people (about half of which are inside the I-270/255 loop, for some context on a map), but only around 3000 residents in its primary Downtown neighborhood (and another 4000 or so in the adjacent Downtown West). These two neighborhoods have a population density that's lower than the city average (and much lower than in the most dense neighborhoods).
By the way, this actually represents a bit of a comeback for the neighborhood. There were only 800 residents Downtown in 2000. Warehouse-to-loft conversions became popular about 15 years ago, which has reversed the trend, at least for now.
That's my fault.