Not an expert at all, but I think this is correct, more or less:
AP is administered by the College Board. (Google them). Teacher has to be "accredited" by the College Board. Not sure what that process entails. Very high level, you take a test at the end of the year, the college decides if your score is good enough to get college credit for that class. Test grade is from a 1 (or maybe 0) to 5. So for example, if you take AP Physics 1, and get a AP test grade of a 3, TAMU might say that is good enough for a physics credit for a history major, but UT would say that is not good enough for a physics credit for a chemistry major.
Dual Credit get your kid a HS and college credit for that class if they pass. Kid graduates HS with a college credit regardless of major or school. (Although I would assume a college that cares about its academic reputation would take a close look at the rigor of the class before awarding that credit, but I don't know).
Not sure about IB, or how it is different/similar to AP or dual credit.
My feeling is that the AP classes are much more rigorous, and harder to get that credit.
tldr: Both are good, take both if the kid can, but AP is probably better, but harder. YMMV.