Valdemar II
Banned
An Austria with South Tyrol and Slovenia is going to be significantly bigger (at least by 1.5 million or so) and wealthier, but it going to have some troubles with minority rights. Depending on what else it gets, the country might have decent access to the Mediterranean, which then increases their wealth that much more, limits Italy really not at all, and increases their independence of Germany economically in the modern era.
A country today of about 9 million people, of whom 1 million are immigrants, I could see Austria being a much more attractive spot for Eastern European immigration (which it is already). The Slovenian area is likely to attract the majority of refugees from the ex-Yugoslavia, though Vienna is still going to be quite popular. Today the nation styles itself the crossroad of Europe between East and West, which would probably be more true if Slovenia is part of country; it would likely increase the nation's involvement economically and politically in the Balkans, as the Slavic citizens are going to be a vital asset in negotiating and connecting with leaders throughout the region.
Quite likely we could see them receive a significant part of the German refugees, and I wouldn't be surprised if many Italians was deported over the border. Which would leave Austria with a Slovenian and Ladin minority.