Mark, one of the things I love about this forum is that it causes me to poke around and explore ideas. Now despite the fact that I had a little fun with it below, the train, seriously, isnt bad at all. Not sure why I would want to go to Berlin, but if I ever did have an "event" its a great option.
The night train to Berlin is 254 to 428 euro, depending on how much risk you want to take, for both of two beds in a cabin. Thats a bargain. Of course its a DB long haul train so you might leave on Tuesday and not arrive until Friday. The cabin has a sink, but you will still arrive sort of ripe. But there are only 19 stops so you will sleep well. No seriously, the last night train I took had about that many and I slept through all of it.
Compared to a flight, the flight would be (for two) $150 to $300 depending on luggage and cancelation requirements. Then a nice 3 star hotel (with a shower) in Budpaest would be right at 100 euro. Then you have taxi to the airport at each end (we will assume for the train its metro), lets say 30 euro in Budapest and 50 euro in Berlin. So a total of 330 to 480 euro vs the train cost.
But the flight will get you in at 11:30, probalby 1pm before you check into your hotel, while the train arrives at about 8:30 (scheduled 7:40 but its DB, so lets be realistic ...... ) which means you will be checked into your hotel (really just drop off your bags) by 9:15 and only have to walk around with a foul odor for 5 hours before they actually let you into the room.