I did the reverse trip, ie Budapest-Bucharest (extended to Sofia when I discovered return flights from Bucharest were at silly times).
I wanted to traverse Transylvania to visit the Saxon towns, which means trains via Brasov (the biggest of the towns, and a major rail junction).
There are several possible routes Budapest-Brasov: via Arad/Sibiu, Cluj/Sighisoara and Cluj/Miercurea Ciuc (the Vienna-Bucharest sleeper runs Arad/Sighisoara).
There are several through trains from Budapest to Brasov, but I wanted day trains - no point in missing the views on the way.
I wanted to visit Sighisoara as the most spectacular medieval town (it certainly is), but found it involved a tight 10-minute change at Cluj, so chose the through train to Sibiu instead.
But in the lead up to the trip, I discovered CFR were closing the route through Sibiu for engineering work for a month, so reverted to Sighisoara instead.
I duly missed the 10-minute connection at Cluj, which meant getting a 42-station evening stopper on to Sighisoara (2 battered corridor coaches and an electric loco).
Anyway, the experience was really great, both on the train and in the towns, and I would recommend the trip - the Transylvanian landscape is just magical.
I stayed overnight in the old town in Sighisoara and then picked up the Vienna-Bucharest train next morning, breaking for a few hours at Brasov which has a very impressive central square.
Just don't expect any trains, especially long-distance ones, to be on time.
Many routes are having major upgrades to give them 160km/h speeds, with long stretches of single-track working right alongside major engineering works.
I think this year the Budapest-Sibiu-Brasov day train only runs in Romania (ie starts from Arad).
The Budapest-Cluj-Miercurea Ciuc-Brasov day train (Harghita) still runs - it serves the largely Hungarian-speaking area of eastern Transylvania.
This is the train I caught, changing at Cluj for Sighisoara.
Unless it's improved, you can only book trains in Hungary 60 days in advance, and in Romania only 30 days (and only reservable ones - not locals).
All quite straightforward on the MAV or CFR sites, producing e-tickets.
Domestic fares in HU and RO are cheap, but cross-border ones are quite high, more like other EC-type fares.
Many trains and most infrastructure (stations etc) are in very poor condition in RO - broken seats and platforms are common.
I did come across the CFR working timetable on their web site, very useful for showing line speeds.
Money (cash) was a bit of a problem in RO.
There are no facilities at the rail border, so you have to find an ATM somewhere, and there are very poor exchange rates (eg 30% charge) when you come to convert lei to anything else.
But it was a memorable trip.
