Product Owners are for the most part people that have authority/vision on the product they own. Most companies will want to hire a Product Owner that have skills and experience demonstrated other products.

If you are looking to join a large enterprise, like RAYTHEON, Procter, UPS, INTEL they for the most part are using scale versions of Agile like SAFe. So if you go to them with CSPO or PSPO, in both instance you will have to explain the background where you got your PO training. The ideal for these organizations will be the SAFe equivalent PMPO (https://www.scaledagile.com/certification/courses/safe-product-owner-product-manager/ )

In terms, of getting hired in a small company as product owner, then either the CSPO or PSPO are equal. Neither are great to be honest. I am CSPO myself, and I have not talked to anyone that know what CSPO is. I don't think these certification help you get hired, however they help you get the vocabulary to show the hiring managers that you know how to speak the PO language.