I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised using Runge-Kutta 4-5).
The Adams-Bashforth method using five previous function evaluations has a global error of $O(h^5)$ (this is the case where $s=5$ in the Wikipedia article referenced below), and requires one function evaluation (per PDE) per step.
The Adams-Moulton method on the other hand requires two function evaluations per step: one for the prediction step, and another for the corrector step. Once again, if five function evaluations are used, the global error is $O(h^5)$. ($s=4$ in the Wikipedia article)
So what is the reasoning behind using Adams-Moulton over Adams-Bashforth? It has an error of the same order, for twice the number of function evaluations. Intuitively it makes sense that a predictor-corrector method should be favourable, but can somebody explain this quantitatively?