The biggest difference between mode C and mode S would be the way transponders are interrogated. Mode C is interrogated in a general manner- i.e. the radar head asks all transponders to reply with their 4 digit code and altitude. The radar head then waits for the responses to get the distance to them. Mode S can send out a general roll-call like that, but it can also interrogate an individual transponder to get what information it needs (a rather large list of things potentially). The biggest advantage of mode S is that individual addressability. Mode C systems can get responses from transponders that were requested by another radar head- leading to them being in different places than expected.