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We present our results on the Chandra X-ray Observatory Advanced CCD Imaging Spectrometer (ACIS) observations of the bright Oort Cloud comets C/2012 S1 (ISON) and C/2011 L4 (PanSTARRS). ISON was observed between 2013 October 31–November 06 during variable speed solar wind (SW), and PanSTARRS was observed between 2013 April 17–23 during fast SW. ISON produced an extended parabolic X-ray morphology consistent with a collisionally thick coma, while PanSTARRS demonstrated only a diffuse X-ray-emitting region. We consider these emissions to be from charge exchange (CX) and model each comet's emission spectrum from first principles accordingly. Our model agrees with the observational spectra and also generates composition ratios for heavy, highly charged SW ions interacting with the cometary atmosphere. We compare our derived SW ion compositions to observational data and find a strong agreement between them. These results further demonstrate the utility of CX emissions as a remote diagnostics tool of both astrophysical plasma interaction and SW composition. In addition, we observe potential soft X-ray emissions via ACIS around 0.2 keV from both comets that are correlated in intensity to the hard X-ray emissions between 0.4–1.0 keV. We fit our CX model to these emissions, but our lack of a unique solution at low energies makes it impossible to conclude if they are cometary CX in origin. Finally, we discuss probable emission mechanism sources for the soft X-rays and explore new opportunities these findings present in understanding cometary emission processes via Chandra. [ABSTRACT FROM AUTHOR]