  We present a consistent analysis of Chandra and XMM-Newton observations of an
approximately mass-selected sample of 50 galaxy clusters at $0.15<z<0.3$ -- the
"LoCuSS High-$L_X$ Sample". We apply the same analysis methods to data from
both satellites, including newly developed analytic background models that
predict the spatial variation of the Chandra and XMM-Newton backgrounds to
$<2\%$ and $<5\%$ precision respectively. To verify the cross-calibration of
Chandra and XMM-Newton-based cluster mass measurements, we derive the mass
profiles of the 21 clusters that have been observed with both satellites,
extracting surface brightness and temperature profiles from identical regions
of the respective datasets. We obtain consistent results for the gas and total
hydrostatic cluster masses: the average ratio of Chandra- to XMM-Newton-based
measurements of $M_{\rm gas}$ and $M_X$ at $r_{500}$ are $0.99\pm0.02$ and
$1.02\pm0.05$, respectively with an intrinsic scatter of $\sim3\%$ for gas
masses and $\sim8\%$ for hydrostatic masses. Comparison of our hydrostatic mass
measurements at $r_{500}$ with the latest LoCuSS weak-lensing results indicate
that the data are consistent with non-thermal pressure support at this radius
of $\sim7\%$. We also investigate the scaling relation between our hydrostatic
cluster masses and published integrated Compton parameter $Y_{sph}$
measurements from the Sunyaev-Zel'dovich Array. We measure a scatter in mass at
fixed $Y_{sph}$ of $\sim16\%$ at $\Delta=500$, which is consistent with
theoretical predictions of $\sim10-15\%$ scatter.
