Yb-doped fibers are widely used in applications requiring high average output powers and high power pulse amplification. Photodarkening is one limiting factor in these fibers. In this paper, characterization of photodarkening in large-mode-area (LMA) fibers is presented building upon our previous work, which indicated that meaningful comparison of photodarkening properties from different fibers can be made as long as care is taken to equalize the excited state Yb concentration between samples. We have developed a methodology that allows rapid and reproducible photodarkening measurements to be performed and that enables quantitative comparison of the photodarkening propensity among fibers with different compositions and under different operating conditions. We have shown that this measurement technique can be used effectively for LMA fibers by employing cladding pumping rather than the more standard core pumping. Finally, we observe a seventh-order dependence of the initial photodarkening rate on the excited-state Yb population for two different Yb-doped fibers; this result implies that photodarkening of a Yb-doped fiber source fabricated using a particular fiber will be strongly dependent on the device configuration.