The easiest and most objective way to do this is by doing something that is extremely difficult to do in the digital domain while being very easy to achieve in the analogue domain. This means complex frequency modulation and all kinds of foldback distortions.. then do this at high pitches. You literally need to be in the gigahertz region of sampling rate to be anywhere near similar results in the digital domain.
.. now run those results through a series of 5 different stomp boxes to further try to duplicate the same sound in digital (you could pick some super common boxes that have been emulated numerous times).
Personally I think it's all rather simple. As long as you have sounds where aliasing and other digital artifacts come into the audible range very quickly, you'll be much better off doing it in the analogue domain. Thus that sound in turn is "analog" vs "non-analog".
.. but are those sounds actually useful and musical? I have absolutely no idea. That's an entirely subjective discussion.
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