How similar are Germany and Austria? How different are they?

[palandio]

The modern (19th century) idea of Germany is not thinkable without a German people, which was mainly defined by language. But the idea of a German people was there before a modern state called Germany (or German Empire) came into existence.
With Austria it's the other way round. Austria was an archeduchy which became the core of the Austrian-Hungarian Empire and its subjects were the Austrians.

The difference between Austria and Bavaria election-wise in my opinion can partially be explained by the following reasoning. Normally the national level is the most important level of political alignment. On the most important level dominant-party systems are rare. Japan might come to mind. India and Israel had dominant-party systems for a generation or so after independence, but then changed. South Africa might follow. Cold War Italy was some kind of an anomal side equilibrium.
Austria's party system is similar to many other developed democracies, since there is no dominant party. The situation with a far-right opposition party and grand coalitions is becoming quite common now, Austria was the avantguarde for this.
Bavaria is not an independent country and hence its party has to be seen in the context of the (historically relatively) balanced German party system. If Bavaria was an independent country it might have developed party system similar to Austria.
If in some scenario of alternative history Austria would have become part of Germany, it might have developed a Bavaria-like party system, with the ÖVP absorbing the Third Camp and various anti-centralists.