acraven, pretty spot on. I know people in love with Prague and those with Vienna and those with Budapest; and they are all correct. Great cities, all three.
Hard to beat the splendor of so much restored and polished in one small area like in Vienna.
Hard to beat the quantity of architecture all in one small area with medieval roots like in Prague.
Both Prague and Vienna are maybe easier visits because everything that most go to see is located in a very compact zone. Of course that means you are mostly among tourists; the tourism density is fairly high, and you get a bit of a Disney feel from that. Just accept that and it’s they are beautiful cities to visit.
A trip to Budapest sort of forces you to live the city and that can be fascinating if you are into cultures and differences. The tourism density is a lot lower because of the size of the “historic district” (there really isn’t one, it’s the whole city).
Here is a guy that discovered Budapest describing how visually pleasurable Budapest is: https://youtu.be/0nd9DuDGCz0?si=aa0c19KaJHEtabkX watch the whole show, its on Youtube too. And a great travel video for Budapest (the same guy has a good on for Vienna too, but notice the difference in his attitude between the two): https://youtu.be/1nd5AtZIrTk?feature=shared
You should travel for interest, not for price, but the reality of getting the best trip for the dollar is always real. So in very broad terms, if your trip to Vienna costs $10 a day, it would cost you $8 a day in Prague and $7 a day in Budapest. Start with hotel costs to get a feeling.
Size and time to reach everything is also important for how long you stay.
General tourism where you go look at the outside of everything and maybe peek in the door briefly: Prague and Vienna you hit the top sights in 3 full days, Budapest will take you 4 full days.
If you love Museums then add a foruth to a half a day for each .....
A bath house a fourth to a half day extra (sort of a living culture museum)
Organized bulding tours, a fourth to a half a day.
In any of the three do take in a cultural evening in a concert, theater, opera, operett. For the layman its equally as good in any of the three cities. Many of the venues are truly beautiful, some are truly local and you might be one of a very few tourists and thats always fun.