Caterina's (it has been discussed many times before) is very very authentic Hungarian, and the food is excellent. As posted in another discussion, the service leaves a little bit to be desired, but the food is great. My family is Hungarian, and my mom is an amazing cook (and brutal critic of Hungarian cooks). When she came to NYC for her birthday in March, I thought we'd take her to Caterina's because my past experiences there had been very reminiscent of eating in Budapest. (as a small aside, we're from Toronto originally, where there was a vibrant Hungarian resto culture until just a few years ago)
Caterina's food did not disappoint, and while I have no idea who's cooking in the kitchen - they have done their research. Now, the proprietors (an older woman, man and their son) are a bit surly, very "straight to business" and do not soften from positive feedback about their food - or - as a result of finding out their patrons are Hungarians (and appreciative). This is pretty unusual, for although Hungarians can be surly people in general - take it from me - usually positive feedback about their cooking warms them up. :)
So, I'd say this: ignore the service and *eat*. Skip the Italian food items. Get into the groove of the piano bar that the place is (the non-food "scene" there is hilarious), and settle in for an awesome Hungarian meal. If you like Hungarian, it's absolutely worthwhile.