It's a nice idea, but I doubt it would work out like that. Austria's stance post-1866 is owed largely to the fact that it was relatively weak and depended on the Hungarians to maintain its stability. An Austria that is powerful enough to dominate Germany would be powerful enough to enforce its rules, and they are not pleasant. There would not be a Kulturkampf - that was a Prussian phenomenon mainly and had as much to do with the need to keep provincials in line as it did with religion. But there is a good chance for Catholic-Protestant tension, and a showdown with the Vatican sometime down the line over the limits of the secular state's rights. What would become an issue, possibly more than under Prussian hegemony, would be democracy and civil liberties. Austria as hegemon of Germany could deploy German resources to keep non-Germans in line in a much more Prussian manner (there is little doubt that it wanted to, looking at the ideas that came out of Vienna). It would also take a much less sanguine view of all the liberalism going on in places like Baden, Bavaria or Hesse. If you want the measure of what Franz Joseph would do given the resources to do it, look at 1848/9.
One certainly can't predict how an Austrian-led Germany would develop. It would depend on a great number of issues, such as whether Austria would keep its posessions outside Germany or not. If it developed from an Austrian conquest of Germany, or through a Paulskirche Grossdeutschland compromise. If it was an absolut monarchy, or introduced constitutionalism. Plenty of scenarios all leading to different results.
OTL both Prussia/German empire and Austria/Austro-Hungary had become more less modern states with the beginnigs of ademocratic sytem, albeit both were flawed. Those flaws were hardly "greater or lesser" in one or the other - they were
different. Was the Prussian system of "no-secret ballot" better than the Austrian system of "divide the parliament into
kurien" or worse? Both essesntialy led to the legislative branches being dominated by large landowners, nobility and businessmen. They were both bad by modern standards, just bad in different ways.
A big question is whether the reforms and policies introduced OTL by both Prussia/Germany and Austria/Austro-Hungary were the results of objective conditions, leading to them being developed regardless who introduced them, or if culture played a factor in it. That is, would a Habsburg-led Brandenburg still create a
Landrecht because it anwsered to the local needs of a north german state? And vice versa?
Austria was relatively weak, but what were the reasons of its weakness? Its multi-nationalism for one. But Prussia faced the obstacle of nationalisms in a way as well - it had to deal with the heimat-sentiments of the non-prussian populations for one. But wheras Prussia decided to deal with it through a Kulturkampf and the development of a Vaterland-setiment (for the lack of a better term), Austria made comprimises with the non-austrians - even in areas where it had the potential of pulling of an assimilation (Burgenland, Czechia). An Austria ruling Germany would too be relatively weak in running it - doesn't it make the probability of it having to deal with those heimat-sentiments in the same way it dealt with the non-germans (suppression at first, comprimise later)? I find that quite plausible.
I imagine religious tentions to be actually weaker in an Austrian-led Germany than a Prussian one. AH was quite multi-religious, with catholics dominating, but it did have its fair share of orthodox (Siebenburgen, East Galicia) and muslims (Bosnia and Hercegovina). Yet religous confilcts were barely present - at least, it is not the first, second or third thing that comes to mind when thinking "Austro-Hungary", whereas Prussia/Germany, despite being much more mono-religious constantly persecuted other religions - catholics, jews, etc. Again, what was the reason? My personal opinion is austrian catholicism simply being more religiously tolerant than prussian protestantism. Thus i find it that when faced with having protestant subjects (especially since they would make a majority), Austria would deal with them in the same way it dealt with the issue at home - introduce tolerance and stick to it.
Civil liberties was something IIRC Austro-Hungary was quite praised for, contrary to Prussia/Germany. While their introduction was eventually the result of a military defeat and the necessity of compromise, it wasn't out of the question even in times when Austria had an upper hand, such as when the October Diploma was suggested. I don't recall the Prussians ever making even a
suggestion of offering something like that. Thus again, even when both were in full force, Austria was more willing to "play nice" than Prussia - even if only by a notch.
Maintaing feudal institutions and noble priviliges etc. surely would last longer under austrian rule, partly due to the different character the austrian nobility had. Its economic reforms also weren't as efficient as the Prussian ones. More poverty is likely to attract more socialists, leading to a reaction of conservatives, probably leading to the system somehow blocking the masses from power like OTL - the tools may be different though.
So I think that while some of the characteristics Austria and Austro-Hungary had were the result of its geographic location (no Ruhr and Silesia meaning less industry, more farmers and peasants etc.) some of them were the result of Austrian culture itself - catholicism, lesser militarism, greater tolerance for minorities, etc. Those traits would not change if the Habsburgs ruled over different peoples, thus some of the characteristics - and I think some of them may be the good ones - would be transplanted onto Germany with a benefit, while other would weaken it. Overall, such a Germany would be
different, though neither better nor worse.
