Looking at heating: There are still (admittedly fewer each year) people heating with coal, often with district heating. This results in approx. 1kg of CO2 emissions per kWh of heat (with losses due to the distribution) (gas heating is 200g per kWh).
The german electric grid has a carbon intensity of approx. 500g per kWh. If you supplement this with a local solar installation that (let's just say) halves the carbon intensity and have a great heat pump setup with a COP of 5 it results in 50g per kWh. This means you can heat 20 times the amount of the worst-case commie-block dweller with coal district heating before it gets even. And even though commie blocks aren't bad, I'd expect modern houses to have much better insulation (at least in Germany) than original commie blocks (worst [reasonable] case, remember).
In cities there is generally less infrastructure per person, but even though there are less road, cable, pipe kms per person, the ones are bigger and/or more heavily used, needing more maintenance and more frequent replacements.
In Germany public infrastructure accounts for 800kg of CO2 per person, while heating and warm water account for 2.2t of CO2. Public infrastructure is important, but so large to matter so much (and remember, this includes things like public service and military that isn't effected by your living style).
Electricity consumption at 0.5t and food at 1.7t are not that different for urban vs rural areas. Other consumption at 3.4t is hard to classify.
Looking at the statistics in Germany (http://www.mobilitaet-in-deutschland.de/pdf/MiD2017_Ergebnis..., page 48) people living in metropolis drive roughly half as much as people living in very rural regions. This is significant, but hardly an order of magnitude. Just because you live in a metropolis doesn't mean you live in a commie block, but I find it hard to imagine it gets down 1/6th. Even people without a car (not only not owning one, but not having access to one) in a metropolis drive 1/7th of people in very rural areas (but commie blocks are certainly not without cars). So this is hardly an order of magnitude.
A car replacement rate of every 3 years also sounds very high to me (ignoring company cars, but that doesn't change in either case), I think 5-6 years at least is more likely for suburbs and maybe a bit higher for commie-block dwellers but I wouldn't be surprised if it's the same.
This was only looking at CO2 (since it's easy to find numbers) and it's undoubtedly true that on average living in dense housing is more sustainable than suburban sprawl or even rural living. But an order of magnitude is huge and much harder to reach.
And since energy usage & emissions are heavily shaped by factors beyond "how dense do you live", it's harder to speak beyond the average. Someone living in the commie block that flies once a year from germany to new york and back produces more CO2 emissions from these two flights alone (~2.5t) than the average german with his mobility (~2.2t).