First the differences have to be audible.

Nonetheless, it is generally the case that if a device has a well
behaved frequency response curve, then it probably doesn't distort
transients very much. Of course you can concoct devices which disobey
this rule (such as echo chambers and goofy filters), but I don't think
they are typically part of a basic audio recorder.

There is a widespread misconception that something is lost in between
the data points measured by a digital recorder. This is not the case.
If the input signal is bandwidth-limited by reasonable analog means,
then the digital data accurately preserves *all* of the temporal
content. (Other experts on this forum can probably state this more
precisely).

Chances are, digital does a better job of preserving timing because the
phase response can be quite flat. Hope this helps.

Michael Mossey wrote:

My *suspicion* is that analog in fact does better preserve the timing
of neural events. However, I would need to know more about
neuroscience and non-linear systems to have a good answer to this,
but
perhaps someone reading is interested.