I believe shenme is more like “what.” Nage, with the 3rd tone (哪个), means “which.” (With the 4th tone, it means “that”).

Alex, I agree with Phil. You actually say in Chinese "WHICH is your favourite Chinese city?", which is different than English. shen2me≈ what na3ge4≈ which Will update if I think of any exceptions.

Here 'shenme' is used for which https://youtu.be/XJXlmvgEQzo