どういうXX here is like English "what kind of XX". It's slightly vaguer with more room for expansion, and could come across as slightly more humble or non-confrontational on the part of the speaker. In terms of rhythm and idiom, どういう状況ですか starts with どういう, immediately indicating that this is a question, rather than 状況は何ですか, where we're halfway through the utterance before there's any hint that it's a question. By starting with a clear question phrase, the listener is primed to think of an answer. This doesn't map very well to English, in that the word orders and emphases are quite different from What kind of situation (or perhaps the more literal translation of how would you say [about] the situation) vs. What is the situation, where the English in all these cases starts with a question word.