Asking which is the "best" is such a loaded question. I doubt that you will find a comprehensive study that would compare the tools head-on. Quality/risk of bias assessment is a subjective/value judgment-based endeavor in itself. Critically analyze the tools that are available to ascertain, within your research group, which tool can best discriminate between and best evaluate the eligible cross-sectional studies - this can vary based on the context of your research topic. Ideally, your reason to choose one over the other should also be explained in the final paper, as part of the systematic review process.
Here are studies comparing various quality assessment tools:
Ma LL, Wang YY, Yang ZH, Huang D, Weng H, Zeng XT. Methodological quality (risk of bias) assessment tools for primary and secondary medical studies: what are they and which is better?. Mil Med Res. 2020;7(1):7. Published 2020 Feb 29. doi:10.1186/s40779-020-00238-8
Zeng X, Zhang Y, Kwong JS, Zhang C, Li S, Sun F, Niu Y, Du L. The methodological quality assessment tools for preclinical and clinical studies, systematic review and meta-analysis, and clinical practice guideline: a systematic review. J Evid Based Med. 2015 Feb;8(1):2-10. doi: 10.1111/jebm.12141
Dreier M, Borutta B, Stahmeyer J, Krauth C, Walter U. Comparison of tools for assessing the methodological quality of primary and secondary studies in health technology assessment reports in Germany. GMS Health Technol Assess. 2010 Jun 14;6:Doc07. doi: 10.3205/hta000085
With the criticism that the Newcastle-Ottawa Scale has received, I saw that the Cochrane tool, ACROBAT-NRSI (“The Cochrane Risk Of Bias Assessment Tool for Non-Randomized Studies”), has gained much prominence and has been highly recommended.
When choosing a tool you should prioritize one that you know how to use and apply correctly.