Prague is Central Europe's best preserved big city, with a
architectural heritage you can't find in any other city to the north
of the Alps.
"Best Preserved" when describing Prague doesn't describe what defines "Best". It has some of the best restored Gothic, Renaissance and Baroque era architecture in Eastern Europe and the largest UNESCO urban zone; and some really great Art Nouveau. Those areas that most tourists go to see stand more as museums than a functioning reality. That and the crowds staring at it is part of the reason that Prague gets the title Disneyland so often.
Prague has an amazing preserved Jewish district, but almost no Jews. Budapest has fewer "remarkable" Jewish landmarks but a thriving and growing and active Jewish community that creates an atmosphere that is hard to find an equal to. Vienna isnt warm and fuzzy on the subject.
In Budapest you wont find much that predates 1800 for two reasons. First, Pest didn't really exist as much prior to 1800 and what was in Buda was bombed flat by the Russians in the final siege of the city. If you were to define "Best" as remaining fully intact and and functioning as originally intended; then Pest probably stands as the best preserved physical and cultural environment; although its not the best "restored" architecture in Eastern Europe. Budapest because of 50 years of Russian oppression was pretty much held in 1945 until just recently so if you want to experience Hungarian culture as it existed in 1945 you can get a pretty idea by visiting today. Not sure the same can be said of Vienna; Prague, maybe. If you have academic background in Architecture, context and function carries a bit more weight which is why I think an Architect might get more out of Budapest than the other two.
Vienna, doesn't have the Gothic or Renaissance presence, but it probably does have the best restored architecture of the three; and yes, it reeks of Empire and if period novels are your thing, this is the place to be. I would argue the statement that it has the best preserved culture. But again, culture is dynamic and so you have to pick a point in history. Or if "preserved" means it has the most dead stuff under glass, then yes, no place beats the sheer number of museums that Vienna has.
For a student of architecture Vienna and Budapest all offer Art Deco, Art Nouveau, Secession (a Vienna creation) and Bahaus Architecture in equal doses. In Vienna and Prague probably better restored, in Budapest probably more functionally intact. In a lot of ways the academic value of these far exceeds that of Gothic or Renaissance; but you gotta sort of study it to understand why.
Point is, there are no Bests. Just differences and those differences will talk differently to different people.