I didn't see an option that reflects my understanding, either.
To me, the ASPH lens has the potential to perform better at the widest apertures. Stopped down to around f/8, not much difference. Or if there is one, the ASPH may render the image a bit sharper, but the image might look "harsh," less pleasing, depending on what I'm photographing. If I want to shoot at f/2 or f/2.8, I'll likely use a Summicron ASPH. At 5.6 or 8, I might use my Summaron or Zeiss c Biogon, or my non-ASPH Summilux. The latter is, IMHO, useless at f/1.4, but stopped down the images are just fine.
Apart from that, you have to go on a lens-by-lens basis. It's a matter of which lens, not ASPH vs. non-ASPH.