We present results from a sample of XMM-Newton and Suzaku observations of interstellar clouds that cast shadows in the soft X-ray background (SXRB) - the first uniform analysis of such a sample from these missions. By fitting to the on- and off-shadow spectra, we separated the foreground and Galactic halo components of the SXRB. We tested different foreground models - two solar wind charge exchange (SWCX) models and a Local Bubble (LB) model. We also examined different abundance tables. We found that Anders & Grevesse (1989) abundances, commonly used in previous SXRB studies, may result in overestimated foreground brightnesses and halo temperatures. We also found that assuming a single solar wind ionization temperature for a SWCX model can lead to unreliable results. We compared our measurements of the foreground emission with predictions of the SWCX emission from a smooth solar wind, finding only partial agreement. Using available observation-specific SWCX predictions and various plausible assumptions, we placed an upper limit on the LBs OVII intensity of ~0.8 photons/cm^2/s/sr (90% confidence). Comparing the halo results obtained with SWCX and LB foreground models implies that, if the foreground is dominated by SWCX and is brighter than ~1.5e-12 erg/cm^2/s/deg^2 (0.4-1.0 keV), then using an LB foreground model may bias the halo temperature upward and the 0.5-2.0 keV surface brightness downward by ~(0.2-0.3)e6 K and ~(1-2)e-12 erg/cm^2/s/deg^2, respectively. Similarly, comparing results from different observatories implies that there may be uncertainties in the halo temperature and surface brightness of up to ~0.2e6 K and ~25%, respectively, in addition to the statistical uncertainties. These uncertainties or biases may limit the ability of X-ray measurements to discriminate between Galactic halo models.
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