In this study, we probe into the roles of exciton oscillator strength and charge of J-aggregates as well as nanoparticle's surface capping ligands in dictating the plasmon-exciton interaction. We systematically compare the plasmon-exciton coupling strengths of two hybrid plexcitonic systems involving CTAB-capped hollow gold nanoprisms (HGNs) and two different cyanine dyes, TDBC and PIC, having very similar J-band spectral positions and linewidths, but different oscillator strengths and opposite charges. Both HGN-PIC and HGN-TDBC systems display large Rabi splitting energies which are found to be extremely dependent on dye-concentrations. Interestingly, for our plexciton systems we find that there is interplay between the exciton oscillator strength and the electrostatic interaction amid dyes and HGN-surfaces in dictating the coupling strength. The oscillator strength dominates at low dye-concentrations resulting in larger Rabi splitting in the HGN-PIC system while at high concentrations, a favorable electrostatic interaction between TDBC and CTAB-capped HGN results in larger exciton population of the HGN-surface and in turn larger Rabi splitting for the HGN-TDBC system than the HGN-PIC system even though TDBC has a lower oscillator strength than PIC. The trend in Rabi splitting is just reversed when the HGN surface is modified with a negatively charged polymer, confirming the role of electrostatic interactions in influencing the plasmon-exciton coupling strength.