Some people say you'll only see the advantage of an apo lens at high magnifications, but when I switched from a 50mm Componon-S, which is a fine lens, to an Apo-Rodagon, I could see the difference in an 8x10" B&W print on VC paper from a 35mm neg.
I think it makes a bigger difference if you are using VC paper than graded paper, because VC paper has a wider spectral sensitivity range (otherwise the filters wouldn't work). It is often said that "graded papers are sharper" than VC papers, and I suspect this is because graded papers may mask chromatic aberration, as they have a relatively narrow spectral sensitivity range.
Apo lenses usually perform better at wider apertures as well, but this is usually not such a necessity with today's fast papers.
Fortunately, darkroom equipment is cheap these days, so you can get the best lenses at fire sale prices on the used market, often in excellent condition.