Harder/stronger/etc aren't properties inherent in the steel, they are also a function of the heat treat. But, the way ATS-34 and AUS-8 are usually heat treated (to 59-61 Rc and 58-59 Rc respectively):
ATS-34 is harder and stronger. That means that on any type job where the edge is pushed into something, ATS-34 will hold its edge better, and also ATS-34 can take a thinner higher-performance edge without rolling.
ATS-34 is more wear-resistant. That means that on any type job where abrasion is the primary way in which the edge degrades, ATS-34 will hold its edge longer. ATS-34 will also take longer to sharpen (unless you've taken advantage of ATS-34's greater strength as explained above, and lowered the edge angle).
AUS-8 is tougher. That means on any job where toughness --resistance to chipping or other damage due to shock -- is a problem, AUS-8 will hold its edge better. Think chopping, etc. Since neither steel is particularly suited to be a chopper, you may not want to over-emphasize this one.
AUS-8 is more rust-resistant. You'll have to decide this one for yourself. If the knife will often be wet, especially with salt water, or is cutting highly acidic food, 8A is attractive.
For a general-purpose EDC folder, ATS-34 will often be the better choice, provided you take advantage of the properties and thin the edge down, which not only brings out the performance better but makes sharpening easier. However, knives made with AUS-8 are less expensive, and the fact is, it's a fine steel for EDC use. Provided the price of the knife reflects the fact that it's made from AUS-8, I do not shy away from it.
Joe