Where did you get the idea that Austria is a socialist country? It used to be to a certain degree, but those times are long gone, except for strong unionization, the social safety net and worker protections. Austria is a deeply conservative country and has been for much of its history. Vienna is a bit of an exception, as it has actually been ruled by social democrats for ~100 years (with a violent break during the 30s and 40s).
Renting is not capped, unless I'm reading your comment wrong and you mean that the city's government influences it. Vienna does not have an explicit cap. Newer flats and houses are index-bound and rents are raised depending on a certain inflation threshold. Older buildings are usually cheaper and there are strict rules on how much rent can be raised. What Vienna does to make renting an apartment affordable is build social housing. Lots of it. 500.000 people in Vienna live in social housing and the Gemeindebauten are actually nice to live in, priority is given to young Viennese still living with their parents, and you can stay in your apartment even if your income increases. The city can therefore bring down rents in the market as not only the poorest can live in these apartments, but they are a valid choice for many.
There also isn't a ban on Airbnb. As someone else already commented, you can still stay at Airbnbs in Vienna. You cannot rent out apartments in social housing as Airbnbs anymore and there are areas in the city where you would have to get a special permit and other inhabitants of the building would have to agree.
As I commented further down, that's true. Although category III is about buildings built before 1953/1945. I just didn't want to give people the impression that Vienna has relatively affordable rents because it has a hard cap on all rents. Newer buildings (not as old as 1953 seems to count as new) with index-bound rents have raised rents quite a bit in the past 5 years and have made Altbau very sought-after.
It's not only buildings built before 1953/1945 though, social housings (Wohnungen in gefördert errichteten Mietwohnungshäusern mit mehr als 2 Mietgegenständen) are capped as well.
Rent in old buildings (Altbau) is capped. The problem is that many landlords don't care and there are no penalties. You can charge back the extra rent but then your landlord will probably not extend your contract...
That is true, but it only affects buildings built before 1953/1945. I just didn't want to give people a wrong impression of why rents in Vienna are relatively low compared to other European cities of a similar size. It's not a "Mietpreisbremse" of hard cap on all rents.
I've also lived in both and Munich is definitely the more expensive of the two and afaik housing affordability is a factor, too. Maybe that played a role.
