The XMM Cluster Survey: An independent demonstration of the fidelity of the eFEDS galaxy cluster data products and implications for future studies

We present the first comparison between properties of clusters of galaxies detected by the eROSITA Final Equatorial-Depth Survey (eFEDS) and the XMM Cluster Survey (XCS). We have compared, in an ensemble fashion, properties from the eFEDS X-ray cluster catalogue with those from the Ultimate XMM eXtragaLactic (XXL) survey project (XXL-100-GC). We find the distributions of redshift and X-ray temperature ($T_{\rm X}$) to be broadly similar between the two surveys, with a larger proportion of clusters above 4 keV in the XXL-100-GC sample. We find 62 eFEDS cluster candidates with XMM data (eFEDS-XMM sample); 10 do not have good enough XMM data to confirm or deny, 11 are classed as sample contaminants, and 4 have their X-ray flux contaminated by another source. The majority of eFEDS-XMM sources have a longer exposure in XMM than eFEDS, and the majority of eFEDS positions are within 100 kpc of XCS positions. Our eFEDS-XCS sample of 37 clusters is used to calculate minimum sample contamination fractions of ${\sim}$18% and ${\sim}$9% in the eFEDS X-ray and optically confirmed samples respectively, in general agreement with eFEDS findings. We compare 29 X-ray luminosities ($L_{\rm X}$) measured by eFEDS and XCS, which are in excellent agreement. Eight clusters have a $T_{\rm X}$ measured by XMM and eROSITA, and we find that XMM temperatures are 25$\pm$9% larger than their eROSITA counterparts. Finally, we construct $L_{\rm X}$ - $T_{\rm X}$ scaling relations based on eFEDS and XCS measurements, which are in tension; the tension is decreased when we measure a third scaling relation with calibrated XCS temperatures.