Cafe Kor is an excellent restaurant. It's one of my favorite spots in Budapest (I lived there for over five years from '98 - '03). I don't know anything about Dio, as it's been a bit over a year since I've last been in Budapest, and have never heard of the place until now.
However, I do give you this phenomenal English-language dining resource on Budapest:
http://www.chew.hu
The Top 33 list of restaurants there is solid. And here's a delightful article entitled
Five Big Reasons Cafe Kor Will Probably Stay on the Top 33 Forever.
Personally, my favorite spots in Budapest were Cafe Kör and Chez Daniel (for French bistro cuisine). For street food, the flour-tortilla-wrapped döner kebabs or falafal from one of the ubiquitous "3 Testvér" ("Three siblings/brothers") chain always hit the spot. Also, there's plenty of great food being served at the markets for cheap prices. Make sure you try some
lángos, which is deep fried potato-based dough, similar to elephants ears except savory, not sweet. They are sprinkled with salt and mopped with garlic water. Sour cream and shredded cheese (among other things) are popular additions, as well.