What is the difference between:
Or in general: When do you use ne and what does it indicate apart from "and you? / what about you?"
1) Reciprocal question: You return the question you have just been asked. It is not limited to you or the other person taking part in the conversation, you can extend your question to 3rd persons.
2） Related to 1) it has a "What about....?" meaning. E.g. you see everybody in your office being handed over some gift. Everyone else is cheerfully distracted, and they overlook the fact that you didn't get anything. You can call attention to your situation with 我呢？ "What about me?!"
3) If not at the end of a question, its role is in amplifying a statement, often with a slight undertone of discontent:
姐姐：我在打电话呢。I am making a phone call. [Can't you see?/Why do you ask?]
4) It can be used to mark continuous tense.
我还在看书呢。I am still reading.
(The previous example is actually also using the 呢 in the same sense, except that in the context it is also amplifying the perceived obviousness of the action, too.)
5) You can use it to express contrast.
I think there is at least one other use case of 呢, I cannot recall.
I think you could use both, but using 呢 is I guess a shorter version, like if you asked:
But it could also go like:
So I don't think there really is a "rule" of when you use it or don't use it. But maybe I'm wrong, I'm only a Chinese 1 student.