I think that Berlin and London passes Vienna even if not much. Of course Vienna would be much bigger city than in OTL.
Yeah I don’t think Berlin and London wouldn’t count as diverse enough like Vienna even with the Racial diversity, it wouldn’t match that diversity of many ethnic groups living in Vienna with highly that TL People would called it “New York City of Europe” Because it has more common with Actual New York City.
I also see before that Vienna will had Sizable Jewish population especially when the Jews from Hungary and parts of the Empire will arrives the City of Music. For reference in OTL 1934 there over 176,034 Viennese Jews in Austria where they living in the Fascist state and What country were significantly‘s smaller.
Now imagine if Austria still have an empire and have Incoming Jewish migrating from parts of the empire as well as a Growing Urban class of Viennese that will be rich through out the 20th Century
It would certainly be one of the most diverse metropolises of Europe, if not else. As for its wealth, it would be in a respectable position, but I don't think it would get the top spot.
Definitely the most diverse metropolis of all in Europe and London/Berlin weren’t even that Diverse compared to what AH Survive Vienna had. They will be people of many ethnic background and cultures that will be alien to even London and Berlin with how many people will habitat in Vienna: Hungarian, Slovenes, Croats, Poles, Ukrainian etc. will be neighbors in the Same Street even tho it would be Racial be overwhelming be White Dominant than New York City or even London/Paris.
As for the Wealth of the AH Vienna, it would probably be the Top 5 of the richest European cities along side with Berlin, Paris, Rome and London with how much Tourists will make to pay Big money to experience the “City of Dreams” as well as Big Investors from the wine industry and many religious groups as well.
Don't forget Budapest, which was also an incredibly diverse and vibrant city - in fact, there was such a large and vibrant Jewish community there that the nickname that it was sometimes given (disproportionately by Anti-Semites) was <German word for Jew>-pest. (Also, 3 of the greatest thinkers of the 20th century came from the same neighborhood in Budapest: Teller, Szilard, and von Neumann - who was one of the Greatest thinkers to ever live - to the extent that they had the same Maths teacher). So it would be more that there would be several great cosmopolitan super-cities in AH, which would be one of the greatest intellectual powerhouses in the world.
I think that Both Vienna and Budapest will the most Diverse city in Europe especially with the Many immigration from Balkans, Eastern and Central Europe. Plus they will have numerous Cultures mixing into the New identity of Viennese and Budapese in 2019 AH. AH Survived Budapest might be called the “Los Angeles of Europe” with it large Jewish community that will highly be as large as French Jews today in over 480,000 or even more. Slovene, Czech, Romanian and German etc would be Habitat in the AH Multicultural Budapest with likely that it will be over Millions more will live in Survived AH.
Remember in 1910 Budapest they were over 200,000 of Jews living there now imagine immigration from Eastern Europe and the Balkans will likely boost Jewish population up by over 3x Time through out the 20th Century