Previous studies on the Cambridge/Sandia stratified burner have produced a comprehensive database of line Rayleigh/Raman/CO LIF measurements of scalars, as well as LDA and PIV measurements of velocity, for flames under non-uniform mixture fraction, under moderate turbulent conditions where the ratio of the turbulent velocity fluctuations to the laminar flame speed is of order 10. In prior work, we applied multiple conditioning methods to demonstrate how local stratification increases the levels of CO and H2, relative to the corresponding turbulent premixed flame, and enhances surface density function (SDF) and scalar dissipation rate of progress of reaction (SDR), based on extent of temperature rise, at a particular location in the flame where the mixing layer and flame brush cross. In the present study, we examine the global features of selected flames at all locations, by obtaining probability density functions (PDFs) for species concentrations, SDRs, and SDFs, conditioned on local equivalence ratio and location in the flame brush throughout the domain. We find that for most cases, species profiles as a function of temperature are well represented by laminar flame relationships at the local equivalence ratio, with some deviations attributable to either differential diffusion near the flame base and local stratification effects further downstream where the flame brush crosses the mixing layer. In particular, CO2 is significantly affected by differential diffusion, and CO and H2 by stratification. However, the stratification effects on the species are relatively minor when conditioned on local equivalence ratio, a simplifying result in the context of modeling. Measurements of the gradient of progress of reaction and scalar dissipation rates, conditioned on local equivalence ratio, show that the thermal zone of the flame is thickened by turbulence: the mean SDF and SDR values are in general lower than those of unstrained laminar flames. The effect is greater under rich conditions, with conditional mean SDR decreasing to less than half of the corresponding laminar value. The extent of flame thickening is the same in the premixed as the stratified case, once the stratified measurements are conditioned on the same equivalence ratio.