paperclip, you still set a Mode A squawk on a Mode S transponder (well at least for now) and the radar system still uses the same Mode A code to callsign conversion (for commercial flights with flight numbers at least). Also, the same conspicuity squawks are still used (7000, 7500, 7600 and 7700 etc.). Mode C is just the altitude part which is the same.
The main benefit of Mode S is the fact that the radar can selectively interrogate a particular transponder (after it's built up a list of all those it can see) rather than getting replies from every single Mode A/C transponder that it can see which can lead to the radar processor getting overwhelmed with replies (and phenomena called garbling and fruiting!).
The extra info you talk about is only available from aircraft with enhanced (I think that's what they call it) Mode S, which is pretty much all commercial air traffic with flight management systems (FMS) on board. Smaller General Aviation (GA) aircraft do not have the facility to send the extra info, but the basic aircraft ID and altitude will be there.
Anyhow, that's way too much info for this thread!
Disclaimer: I start college next week and it's been a couple of years since I did ATPL theory, so some of this may be slightly wrong or a little too simple. Caveat emptor.