Thats quite an generalisation you made.
Especially the "Younger" Habsburgs (Franz Ferdinand among them) were driving for "modernisation".
FF don't really strike me as a 'liberal' more on 'divide et impera' type, favoring modernisation of the country from the economic pow but from the political i can see him promise things but not really be ready to give up power.
Karl seem more pliable but with less drive, more a reactive one than someone with a clear plan.
Rudolf, i don't know enough about him to say anything, except that a man who commit suicide will hardly resist the enourmous stress of be a head of state (but this his my personal and professional opinion regarding who commit that act that a clear analysis of the Rudolf characther)
Unfortunately you are right for Franz Josef.
If he suppress the Magyar will be probably as an example for all the other to shut up and to as they are told, good in the short time and very bad on the long term.
Rudolf actually was leaning towards liberal views and Hungary. making Rudolf emperor in 1887(?) would give Austria time to solve some issues - especially the nationalities - a liberal emperor might give more rights to minorites and the major nations. In addition if his inclination for Hungary might allow him to steer clear from Prussia.
Its hard to see where his reign would have steered, but you might assume he would stter a differennt course than his fatherm so austria would have 25 years to get modernized before OTLs First world war.
Assume he steered a pro French and pro British course (no interest in colonies) while maintainigt a "distant" friendship to Germany. This in turn might enable Germany to maintain more cordial relations to Russia.
Russia would still be somewhat hostile to Austria. In effect you would have a less rigid system of alliances which would help to "defuse" conflicts.
If you like you could come up with an Austrian/Russian conflict (over Serbia) that triggers a greater war
Russia
Germany (Rückversicherungsvertrag prolonged)
Italy (friendly to Germany and opposed to France)
vs.
Austria
UK (concerned by Germanys naval programme, allied to Japan which is still hostile to Russia)
France (opposite Italy)
Turkey (enemy of Russia)
Just for fun.
Well with this kind of alliance there are a lot of possibilities of conflict, regarding Austria, assuming Conrad or a man with similiar view being in charge, the possibility of a war with Italy are big (Conrad hitched for a fight with Italy) so things can go down from there. The Balkan war or the Ottoman-Italian war can escalate, hell even the Russo-Japanese war can bring the conflict in the open and in this case a German-Russo alliance is an hard one to beat in a land war in Europe
But at the end of the war (assume US joins in on UKs side) with the Austrian side victorious (though Austria would be hard pressed - enemys on all sides) the victors could demand the spoils of war... Austria COULD want Venetia and create an Lombardian puppet/buffer state...
COULD is on thing, and sure Vienna will want it plus maybe a the Lombardia buffer, but as the aftermath of WWI demonstrated what you want and what you can realistically achieve and keep are two different things; expecially after a long and difficult conflict.