IB is generally considered more work. While AP courses are targeted to common frosh level US university courses, IB courses may differ somewhat in content.
For IB math, choose the A&A versions over the A&I versions for a student going into a math-heavy major in college. HL obviously covers more advanced material than SL, and is more likely to get subject credit and advanced placement in college (check colleges’ web sites for how much subject credit and advanced placement each IB and AP exam and score may give).
Here is an example of what the UCB math department gives / recommends:
https://math.berkeley.edu/courses/choosing/high-school-exam-credits
(Math 1A, 1B = single variable calculus; Math 10A, 10B = calculus, statistics, and mathematical methods for biology and medicine; Math 16A, 16B = calculus for business majors)
| Exam | Score | Subject credit |
|---|---|---|
| AP calculus AB | 3, 4, 5 | Math 1A |
| AP calculus BC | 3, 4 | Math 1A |
| AP calculus BC | 5 | Math 1A and 1B |
| IB math A&A SL | any | none |
| IB math A&A HL | 5, 6 | Math 1A |
| IB math A&A HL | 7 | Math 1A and 1B |
| IB math A&I SL | any | none |
| IB math A&I HL | 5 | Math 16A |
| IB math A&I HL | 6, 7 | Math 10A or 16A |