We present the result from fitting XMM-Newton observations of the Anomalous X-ray Pulsar 1RXS J170849.0-400910 with the four different magnetar emission models of Taverna, Turolla, Suleimanov, Potekhin, and Zane (2020). The models include a blackbody model, a magnetized atmosphere model, a free-ion condensed surface model, and a fixed-ion condensed surface model. Compared with earlier analyses, we perform here for the first time a phase resolved analysis. The fixed-ion condensed surface model gives the best description of the data, followed by the blackbody and free-ion condensed surface models. The magnetized surface model fits the data rather poorly. The theoretical models predict not only the flux energy spectra (Stokes I), but also the polarization fraction and angle energy spectra (Stokes Q and U). The models thus allow us to generate simulated data sets resembling the ones that will be taken with the Imaging X-ray Polarimetry Explorer (IXPE) mission scheduled for launch in October 2021. Based on the analysis of the simulated data sets, we explore the discriminating power afforded by the X-ray polarimetry information, and discuss the prospects for IXPE giving the first clear detection of strong-field Quantum Electrodynamics (QED) in the signal from an astrophysical source.