It's between 16 and 18 hours driving if you drive straight between the two cities and don't run into too much traffic, which is probably two days worth of driving. You'll want to plan on more time if you plan on stopping to see the sights along the way, or expect trouble with traffic.
At slightly over 1,000 miles, it requires about 16 hours of driving. This takes you through Belgium, Germany, Austria, and Slovakia before getting to Hungary.
This drive would take about 16 and 1/2 hours. During the drive you'll go through France, Belgium, Germany, and Austria. After driving on the many toll roads, you'll then arrive in Hungary.
Me and my boyfriend have done this a couple of times, it takes 17 hours with a few comfort breaks to stretch your legs a bit. If you go buy coach (witch is just plain awful) it took us 29 hours! I do not recommend eurolines!