We report a measurement of the ratio of dimensionless enhancement factors κ0 for Cs-129 Xe and Rb-129 Xe in the temperature range 115 − 140 • C; both pairs are used in spin-exchange optical pumping (SEOP) to produce hyperpolarized 129 Xe. κ0 characterizes the amplification of the 129 Xe magnetization contribution to the alkali-metal electronic effective field, compared to the case of a uniform continuous medium in classical magnetostatics. The measurement was carried out in "hybrid" vapor cells containing both Rb and Cs metal in a prescribed ratio, producing approximately the same vapor density for both. Alternating measurements of the optically detected EPR frequency shifts caused by the SEOP polarization and subsequent sudden destruction of the same quantity of 129 Xe magnetization were made for 133 Cs and either 87 Rb or 85 Rb. An important source of systematic error caused by power fluctuations in the pump laser that produced variable light shifts in the EPR frequency was characterized and then mitigated by allowing sufficient warm-up time for the pump laser. We measured (κ0)CsXe/(κ0) RbXe = 1.215 ± 0.007 with no apparent temperature dependence. Based on our previous measurement (κ0) RbXe = 518 ± 8, we determine (κ0)CsXe = 629 ± 10, more precise than but consistent with a previous measurement made by another research group.