In this paper, we present and compare two approaches to model supply and demand curves of a sealed-bid auction market. Both the linear hinges model and the sigmo model are able to extract the relevant information from these bidding curves, without losing significant market information. We discuss their main similarities and important differences using a unified framework, to highlight their main strengths and weakness. A practical comparative study based on real supply functions from the Californian electricity market has been included to derive practical conclusions.