My take is that one of the main reasons for the ransom system is to encourage Players to surrender rather than fight to the death, so the details should support that.
Generally players hate losing gear, often more than losing the PC entirely, in which case the default would be that ransomees keep their gear. That said, I would ask your players when first explaining ransoms, or as a Session 0 question, how they want it handled in your campaign 'cos this seems like a YGWV issue.