I don't understand, what kind of a difference? Winamp has an EQ, are you using one of the weird presets or something?
I don't think you can use ASIO drivers with regular audio programs like Winamp, I'm pretty sure they only use WDM. However there should be no audible difference in the actual audio, whether played back with ASIO or WDM drivers. You may prefer ASIO drivers for audio apps like Cakewalk if it offers lower latency, or maybe your hardware has better ASIO drivers than WDM, but in terms of the actual sound, i don't think there should be any difference at all.
Also, could it be possible you are hearing a difference due to different sample rates or bitrates?