Spectral diagnostics for IXO

IXO with its high throughput and spectral resolution will allow X-ray spectroscopy to become a standard working horse for astrophysics. The grating spectrometers on Chandra and XMM-Newton have opened the field, but due to their limited effective area only for the brightest sources and due to the way that gratings work only for point sources or very compact extended sources. With IXO, the effective area increases by 3 orders of magnitude with roughly similar spectral resolution. Due to the use of imaging TES arrays, also extended sources can be studied without complexities. The current design of IXO is based on both a calorimeter array as well as a grating spectrometer. In this document we compare the performance of both types of instruments for different astrophysical situations in a generic way.