I think the only time an APO lens comes into it's own, is with ginormous colour prints. Basically they cut out the colour fringing, compared to a non APO lens.
I have actually seen a 50 Componon S and a Rodagon APO 50 go head to head. There was a difference that you could detect using a Bestwell grain finder, the image looked snappy as hell on the baseboard and the 20x enlargement prints were different.
We were enlarging colour negative material, as that is my main enlarging medium.
The APO was ever so slightly better than the Componon S. However I purchased the said Componon S lens, it resides in my enlarger to this day, almost 16 years after the test.
If I remember correctly, the Componon was about ½ the price of the APO lens, that was also a mitigating factor!