+1 to everything Danny said. Put another way, a multiband compressor is preferred to mitigate frequency anomalies that are not constant. We're talking primarily about resonances, which might cause a specific frequency range to sporadically be too loud. Statically dipping the range with an EQ might hurt the sound everywhere else that it's not a problem.
There is a third class of processors that combine the features of both multiband compressors and equalizers, and that is the dynamic equalizer. Check out meldaproduction's
MDynamicEQ, an inexpensive plugin that you can demo. Once you get over the fairly steep learning curve, it's a great tool for those situations where neither a multiband nor a conventional EQ quite fills the bill.