We show that both types of coupling are robust to detuning, and establish a phase relation in a similar time scale. We also show that significant difference in condensate population and formation arise under imbalanced optical pumping. The provided dataset contains the experimental data used to generate the figures in C. Toebes, M. Vretenar, J. Klaers, Dispersive and dissipative coupling of photon Bose-Einstein condensates, arXiv:2110.01898 [cond-mat.quant-gas].

The data consists of text files, representing measured photon densities, both time-averaged (with a CMOS camera) and time-resolved (with a streak camera). As well as relevant integrated intensities and calculated visibilities derived from this data (as used in the manuscript). A 'README.txt' is provided in the main directory that provides further details.