© 2015 American Physical Society. Electrically neutral massive color-singlet and color-octet vector bosons, which are often predicted in theories beyond the Standard Model, have the potential to be discovered as dijet resonances at the LHC. A color-singlet resonance that has leptophobic couplings needs further investigation to be distinguished from a color-octet one. In previous work, we introduced a method for discriminating between the two kinds of resonances when their couplings are flavor universal, using measurements of the dijet resonance mass, total decay width, and production cross section. Here, we describe an extension of that method to cover a more general scenario, in which the vector resonances could have flavor-nonuniversal couplings; essentially, we incorporate measurements of the heavy-flavor decays of the resonance into the method. We present our analysis in a model-independent manner for a dijet resonance with mass 2.5-6.0 TeV at the LHC with s=14TeV and integrated luminosities of 30, 100, 300, and 1000fb-1 and show that the measurements of the heavy-flavor decays should allow conclusive identification of the vector boson. Note that our method is generally applicable even for a Z' boson with non-Standard invisible decays. We include an Appendix of results for various resonance couplings and masses to illustrate how well each observable must be measured to distinguish colorons from Z's.