Generally the detection limits in XPS range from 0.1 to 1 at%., but there are instances there these limits can be improved or be considerably worse.
In 2014, Alex Shard at NPL has published an article investigating the detection limits of elements in over 6000 binary systems for Al and Mg excitation sources. As the paper demonstrates, heavy elements (e.g. Pt) in a light elemental matrix (e.g. C), then detection limits are closer to 0.01 at%. For the reverse system, the detection limit of C in Au would be in the order of 3%, however as the paper demonstrates limits of 10% are not uncommon!
The paper also highlights the problems of spectal overlaps can significantly reduce the detection limits. Changing excitation sources (Mg instead of Al) can aid the shifting of peaks to minimise this issue or careful and advanced curve-fitting models can overcome some of these issues.
 A.G. Shard, Detection Limits for XPS for more than 6000 binary systems using Al and Mg K X-rays, Surf. Interface Anal. 46 (2014) 175-185. https://doi.org/10.1002/sia.5406