Does AP classes or actual college classes taken at community college look better on a Harvard application?
Short answer - it depends.
If the material is identical, e.g. calc 1 vs AP Calc AB, then usually the AP course makes more sense. If you’ve exhausted your HS curriculum, then usually a n advanced college course makes more sense.
Also depends on where you take the course. AP is a defined and well-recognized curriculum, so schools are very comfortable with what it means.
Calculus 1 at a community college is an unknown and probably wouldn’t be as attractive on an application. At our HS, there is the option for dual-enrollment “College In High School” Calculus with out local CC, and it’s definitely a step below the AP course.
Taking an actual course from a known major college, Calc for Science/Math majors, not Calc Intro for humanities majors, would probably be looked at on par.
A course past the normal AP courses, or beyond what your school offers, are great, but in those cases your really don’t have an “AP or college” choice.
To assess a calculus course at a local community college, try seeing if your state flagship university accepts it for subject credit (for math, physics, or engineering majors, not just business majors) if you transfer it there.
For other courses, you may similarly want to check if the course is accepted for subject credit for those majoring in the subject (or at least those in your intended major).