Using Chandra observations, we derive the YX proxy and associated total mass measurement, M_500_^Yx^ for 147 clusters with z<0.35 from the Planck early Sunyaev-Zeldovich catalog, and for 80 clusters with z<0.22 from an X-ray flux-limited sample. We reextract the Planck Y_SZ_ measurements and obtain the corresponding mass proxy, M_500_^SZ^, from the full Planck mission maps, minimizing Malmquist bias due to observational scatter. The masses reextracted using the more precise X-ray position and characteristic size agree with the published PSZ2 values, but yield a significant reduction in the scatter (by a factor of two) in the M_500_^SZ^-M_500_^Yx^ relation. The slope is 0.93+/-0.03, and the median ratio, M_500_^SZ^/M_500_^Yx^=0.91+/-0.01, is within the expectations from known X-ray calibration systematics. YSZ/YX is 0.88+/-0.02, in good agreement with predictions from cluster structure, and implying a low level of clumpiness. In agreement with the findings of the Planck Collaboration, the slope of the YSZ-D_A_^-2^Y_X_ flux relation is significantly less than unity (0.89+/-0.01). Using extensive simulations, we show that this result is not due to selection effects, intrinsic scatter, or covariance between quantities. We demonstrate analytically that changing the Y_SZ_-Y_X_ relation from apparent flux to intrinsic properties results in a best-fit slope that is closer to unity and increases the dispersion about the relation. The redistribution resulting from this transformation implies that the best-fit parameters of the M_500_^SZ^-M_500_^Yx^ relation will be sample-dependent.