hey gb, in my opinion all of the products you mentioned will give you about the same results as far removing swirls goes. I haven't had much luck removing swirls with any of the products that you mention except for very, very light swirls/scratches. on an abrasive scale all three are basically non-abrasive and you can't fix paint problems with them, you can just clean paint with them.
i had a friend with a black car that had water spots. we used aio and after much rubbing the spots were still on the car. we grabbed a clay bar and it removed the water spots in one pass. does this mean clay is more aggressive than aio?
i had two different situations where i had cars that were heavily oxidized. what was the best product for removing oxidation? 3M imperial hand glaze took off the oxidation quicker than anything else we tried (we tried aio and finish first as comparisons). does this mean that 3m imperial hand glaze is more abrasive than aio?
i'm not arguing anyone's theory, just offering my observations and some food (detailing food that is) for thought. i have pictures of one of the oxidized cars, well gmc jimmy actually. i'll find a scanner and show them to you.