I would say Romanian, only because, from my limited knowledge of both languages, I believe it will be easier to learn, that is you will make faster progress.
Romanian is a romance language after all, and while it's pretty distinct from other romance languages, it still derives most of its grammar and vocabulary from a familiar Latin/Indo-European source.
Hungarian is not a romance language, in fact it is not even an Indo-European language; it's Uralic. So, unless you speak Finish or Estonian, Hungarian grammar and vocabulary are fundamentally different from anything you have experience with. You might as well learn Japanese; it might even be easier to learn than Hungarian.
Of course, that's assuming that you A) don't have a bias towards of side of the family and B) can't just learn both.
If you are a lot closer to the Hungarian side of your family, you should learn that.
People often say you shouldn't learn two languages at the same time, but in my experience as long as they are different enough it won't cause any confusion (your only problem would be time management); I've been learning three languages at the same time (Spanish, Japanese, and German) for years; it doesn't cause me any real trouble. From my understanding, Romanian and Hungarian are definitely different enough that it shouldn't cause any confusion.