Services ISM is economically more representative but historically less market-moving, partly because it has a shorter history and partly because it is less cyclical and so gives fewer clean signals.
Its prices paid component is the one to watch in an inflation cycle, since services inflation is what determines whether core-pce gets back to target. The employment sub-index also acts as a partial preview of the services portion of nfp.
Example: manufacturing ISM at 47.5 and services at 54.0. Weighting roughly 20% manufacturing and 80% services gives a composite near 52.7, which is consistent with modest growth rather than the contraction the factory headline implies.
Related: ism-manufacturing-pmi, pmi, sp-global-pmi, core-pce, diffusion-index