Translation:To which restaurant are we going, to this Chinese or to that Japanese?
English is being difficult again.
I'm not exactly sure about that but I feel like "What restaurant" is actually asking about "What kind of restaurant". So more about a category than a single entity. That would be translated as "Milyen étterem" in Hungarian.
Edit: I mistyped.
"What restaurant..." is fine - it depends on the speaker's colloquial use of English - everything has its context.
Even the "what kind" inference still works, as this one is Chinese and that one's Japanese.
As a native speaker, if I was getting flustered by others' indecision - I'd say something like: "So, what restaurant are we going to? The Japanese or the Chinese one? Which one are we going to?"