In general, CSCs are considered to harbor high potential to repair DNA damage under inflammation and ROS in the tumor micro-environment. On the other hand, given that some kinds of tumors arise from CSCs with accumulation of genetic mutations, the genomic instability in CSCs is likely as compared with non-CSCs. In my opinion, the potential of DNA repair in CSCs might be different each other at the carcinogenesis and during the tumor development including invasion/ metastasis and relapse. I mean that pre-malignant cells with higher genomic instability would be CSCs, and furthermore, CSCs later acquire rapid DNA damage repair potential.
Although I havent seen a manuscript of higher genomic instability in cancer stem cells, given that CSC and Non-CSC are interconvertible, the genomic instability does not seem to be very different. Further interconversion happens in a few days (2-8 days depending on the assay) which in my opinion is not enoughf time for acquisition of genomic instability. In a way, I do second the answer by Yoshida. The difference potentially is "epigenetic".