The first one enquires if the listener is living in the apartment at present.The second one is a question of simple present type which deals with more obvious or general facts(here,is the listener’s living place still the same?).So,it seems to me that both are appropriate to use as both implies the same thing.
The questions are synonymous. Both ask the person if they continue to live in that apartment.
If I read "Are you still living in that apartment?" in a novel, I might assume a degree of deprecation. Of course when speaking the tone of voice is important.
Sally: Hello John, haven't seen you for ages. How are you?
John: I'm fine. How are you? Are you still living in that apartment?
Sally: I know. I still have arguments with the landlord nearly every time I see him.
Note: This is subjective and others may not agree.