Upvote:2
Both cities have their charms. Personally I think you should compare Vienna, Budapest and Prague. The Lonely Planet even has an edition on Budapest and Prague. To come back to your question, since you say that your dad likes architecture, I would go for Budapest. Its parliament, castles and also its thermal baths are a lust for the eye. Furthermore its bridges over the Danube river are impressive. If you prefer music over architecture I would go for Vienna.
Depending of the time available, you could choose to do both. Both cities are within 3 hours from each other by train.
Upvote:8
Definitely Vienna is easier to navigate, public transportation is better and easier to use, more people speak English, and architectural highlights are all concentrated within a 4 mile radius. Vienna also has more high-quality large art museums, and overall, it's more tourist-friendly than Budapest.
However, Vienna is not as strikingly different to other Western European cities. In contrast, Budapest has one of the most flamboyant parliament buildings in the world, Byzantine (orthodox Christian) churches, beautiful bath houses, and many sites linked to interesting tales from the times of the Soviet-controlled communist regime.
Two amazing cities, both on the Danube, but very different.
If you are still undecided, I recommend you stop by a bookstore and --without buying it-- grab a copy of The Lonely Planet guide for Europe. The intro paragraph to each city gives a very good and general idea of what the city is like.