I have whole bunch of enlarging lenses and have made thorough comparisons in the past. Here are my observations:
The very best lenses for 35mm are not labeled "APO" at all, but they do provide exceptional Resolution within the whole visible spectrum. These were lenses originally designed for microdocumentation, like the Zeiss S-Biogon 5,6/40 or the Zeiss S-Orthoplanar 4/60. Unfortunately, they are out of production for a while and are rare items on the market.
You will hardly be able to tell the difference between an APO and non-APO in the center of an image, even at magnification ratios up to 20x. If you think you can, make a double blind test. Your observation may be influenced by some placebo effect.
You will be able to see a difference between an APO and a non-APO lens in the outer image areas, if and only if: your enlarger is well adjusted (i.e. negative stage, lens board and easel are exactly parallel) and your negatives are sharp edge to edge (i.e. your shooting lenses are good, too). In case of doubt, make a simple test: just shift a negative in the carrier such that an edge will become the center (in respect to the lens). If the result is much better, either your enlarger is out of adjustment or you may really benefit from a better enlarger lens. If you canít see any improvements, double-check the edge sharpness of your negatives with a good loupe. The strength of the chain is always determined by the weakest link.
An APO lens may reach its best performance at only one f-stop down. A non-APO lens usually requires two f-stops. In addition, some APO lenses are faster than their six-element counterparts (which is not the case with small format lenses). A larger aperture usually provides more resolution, which is an advantage at higher magnification ratios but might be visible at standard magnifications, too (eye resolution can be as much as 15 seconds of arc in special cases like nonius vision or very high contrast details)
APO lenses are multicoated (whereas most six-element lenses on the (used) marked are only single coated). They provide better contrast, esp. at higher magnification ratios. Half a paper grade is not uncommon. And this might not always be an advantage! Last but not least: not all pictures benefit from better sharpness/resolution (one reason to have more than one enlarger lens Ė and one reason to seek for older ones, too)
With only few exceptions, the magnification ratios recommended by the manufacturer do not differ significantly between APO and non-APO lenses. Outside these ranges, an APO lens will not perform much better than a non-APO lens. So APO lenses are not always better suited for big enlargements (apart from the inherent limitations of the 35mm format here). For murals, a special six-element Rodagon-G will perform better than an APO-Rodagon or APO-Componon. Not only on paper specs, but in practice, too.