Vienna — Hungary, already the East bloc's avant garde in domestic reform, has begun setting a trendy cultural pace, too. This summer, Budapest saw ''Cats,'' ''Jesus Christ Superstar,'' and its own homespun musical, ''Stephen the King.'' Residents even filled in as extras in some extravaganza concert scenes from a rock movie made by American, British, and Hungarian film companies.
All this has given the Hungarian capital a certain revival of traditional ''one-upmanship'' with its old rival and twin capital of the Hapsburg Empire, Vienna.
The shared imperial splendor ended just 65 years ago. Today the cities represent two very different worlds - Vienna, the capital of a neutral Austria which identifies with the West; and Budapest, the capital of a republic that is tied fast to the Soviet bloc.
But the historical affinity and the old sentimental ties remain on both sides. (When Hungary's Marxist rulers built a Danube bridge to replace one destroyed in World War II, they gave it its old name, the Elizabeth, after Francis Joseph I's beautiful empress.)
A decade of Hungarian ''liberalization'' has meant changes in which Budapest has recovered much of the flavor of its old life style - and in the process developed a modern image that is often as ''with it'' as Vienna's.
The latest feather in its cap was its production of Andrew Lloyd Webber's musical ''Cats.'' It prompted recall of an old Hungarian claim that the Budapest theater was always one move ahead of the Viennese.
Budapest was not only ahead of Vienna. It gave ''Cats'' its European premiere. When a London critic wrongly credited Vienna's Theater an der Wien with this distinction, the British ambassador in Budapest wrote to the Times (London) to put the record straight.
As Ambassador P. W. Unwin pointed out in his Sept. 29 letter to the Times, when Vienna mounted the show in late summer, it had played ''to enthusiastic audiences here (in Budapest) for months.'' Some 30,000 people had already seen 35 performances, and business was still booming.
Earlier in the year, ''Jesus Christ Superstar'' was the first rock opera to reach the Hungarian screen and, although it was years after the musical's Western debut, it still put Hungary out in front of its allies. They have yet to give the show official approval.
The Hungarians have since made their own rock-opera movie. Its ''Superstar'' is ''Stephen the King,'' the country's patron saint and national hero.
It tells of the Christian monarch who founded Hungary in 1001, and whose golden crown was returned to Hungary (from postwar custody in the United States) in 1978 to again become the symbol of the country's past.
The past has been the evocative theme of a flurry of books and movies in recent years. Gabor Koltay's production of ''Stephen,'' revolving around the King's Christianization and conflict with the leader of a pagan revolt, caught a contemporary mood of awareness.
It drew deeply emotional response from its audiences. Its historical authenticity was not questioned. But it was ideologically controversial for some of the Communist Party press, since the implicit analogy between past and present upset the ultradogmatic. Still, the film's message seems to coincide with the concept of national identity that forms an essential part of the ideology surrounding Hungarian party leader Janos Kadar.
The kind of conflict mirrored in his movie, Mr. Koltay said in a newspaper interview, ''does not become obsolete in the course of time. The question of how a small nation finds a way to survive is always valid.''
Also this summer, the Hungarian-American makers of the rock ''horror'' movie, ''The Predator,'' decided to go public on location. So a dramatic sequence - complete with two famous American rock bands - was shot in a village outside Budapest.
It drew a mammoth ticket-paying audience of young fans who also made additional extras and to whose delight the show went on into the night. All for nine minutes of actual film.
A Budapest paper called it ''an East-West commercial coup.'' It was. Shooting cost a quarter of what it would have cost in the United States, and the 250 Westerners engaged in the production left $1.5 million behind with Budapest hotels and other services.
The movie was very much in line with Hungary's increasing encouragement of private initiative. By the end of 1982, for example, more than 17,000 small tradesmen were operating, with official approval, in a private consumer-services sector. Private builders did 40 percent of all housing construction.
Such freedom is not yet evident in internal politics. But a new law for the elections due in 1985 ensures that two or more people will run for every elected office - from parliament to town and village councils.
This is not a breakthrough for political plurality. A candidate will still need the nod of the Communist Party. But voters will be able to show a personal preference for an ''independent'' candidate. It seems genuinely intended to be a first step to broaden participation in public affairs just as, in the economy, reform already allows workers to operate small production units of their own on the margins of a state enterprise.