Just from practical experience it seems the former (two pitches on one distorted electric guitar) is nosier than the later (the two pitches on separate distorted guitars.) I don't know this is actually the case, but it seems so.
An example could be playing a passage in thirds around middle to high range. On one guitar those thirds seem to get very muddy and noisy. But if the parts are on separate guitars it seems less noisy.
Can someone elaborate on what happens in those two scenarios in terms of electric signals and acoustics? If there isn't really a difference, that would be helpful to know too.
Re. two separate guitars: I was thinking two separate speakers or two separate recorded tracks.