There really is no difference between quis used adjectivally and qui. Your take that it can or should be read in the sense of "qualis", i.e. what that day will look like, seems fine to me, but it doesn't really hinge on whether the author uses qui or quis. They're interchangable.That's true.
But qius day would I then understand like "which day =which of many possible days'' would that be, but qui dies I would understand as "what kind of day =what will this day look like". Is my understanding of these pronouns wrong? It would seem more logical to me that Vespasian is pondering the second option als what it will be like ...