If you could not visit both cities, which would you recommend more highly, Prague or Budapest?

Prague is far better. I like Budapest, it is much bigger city than Prague, has better weather and it cheaper, but the quality of the services lags, and there is as not many things to see unlike Prague. Prague has one of the largest medieval quarters in all of Europe comparable to Rome and it has far more sights (castles, monasteries, palaces, bridges) than Budapest. Much of the Budapest was build in the 19th century. While its Buda castle is indeed impressive, there is not much to tour unlike at Prague castle where you have second largest Gothic cathedral in Central Europe in one of the largest castles in the world. Additionally, Budapest was ruined in the 20th century, so there are scars from the war unlike Prague. If you like 19th century architecture in city with wide boulevards, go to Budapest. If you like medieval art and style you go to Prague. If you have less money to spent go to Hungary where the exchange rate is much better. If you want better services for your money, go to Prague.

Prague is much more scenic. It has a medieval old town core. There is a lot to do in Prague. I visited Budapest on a couple of occasions and was dissaponted both times. The food was terrible. The city is a bit grubby - and that is being generous.

Prague, far and away. Budapest has some interesting history, but Prague is a beautiful, walkable city with lots to do.

Both are beautiful but I like Budapest better. It's a bigger city, it's less touristy, and the spas cannot be beat. You can see Prague in an afternoon, it takes a few days to see all of the sights in Budapest. Plus I had much better food in Budapest. I mean Michelin quality food for about €20 per person including a glass or two of wine or beer

If you could visit both it will be the best, since both of them are very beautiful. Of course, Prague is easier to walk about and around, but also smaller in size.

Both have a river that flows in their middle and that alone is a lovely scenery.

Berlin

budapest, they have mineral pools in the center of the city