hello, we just got back from both cities on our last trip in April. Have been to PRG twice in the last 6 months, and decided not to miss BUD this time around.

The two cities are like comparing "apples And oranges" so to speak, but I wouldn't miss either one if you have the chance. Flying is great, but I understand the train is really cheap, if you have the time, and what I remember being told it's only a few hours longer. (We flew)

This is only one opinion of course... Budapest is a much larger city, a little more "intimidating", and more "Eastern" as we considered it. Both cities have a wealth of history and are equally beautiful compared to each other. We thought the nightlife is smaller in Budapest, and not as cosmopolitan as Prague is.
While Prague is a smaller city, the night life is more vibrant than Budapest.
However, if you go to Budapest, there is a drag bar there downtown, you dont want to miss, it's a hoot. Like something out of say "from the 70"s" for example, not out of intention, but for real.

Budapest we found a little scary at times, compared to how we felt in Prague. We met an American friend and first time visitor who had no fear, but found himself in a situation he had to get out of safely one night in a car, (jumped out, but leave that to the imagination). If you stick together, you should be just fine using common sense and not going to far into the ("suburbs" for lack of a better word) in Budapest.
Have fun and enjoy your trip!