......some people installed ASIO4ALL which looks like an ASIO driver but sends output to a low level interface (kernel streaming) rather than to the audio hardware like a real ASIO driver. There are two practical reasons why this is less desirable than an actual ASIO driver: The ASIO4All module hasn't been tested with most audio devices that it will be used with. And the kernel streaming interface is far less tested as an entry point for the audio stream than Wave Out, DirectSound or ASIO......

Old Listener

That being said, not only can I hear a difference in software players, but I can hear a difference in the ASIO plugins for them.  This Japanese code writer made some really nice ASIO plugins for both Winamp and Foobar, which sound way better than the stock ASIO plugins.
http://www.un4seen.com/forum/?topic=8980.15

In Reply to: RE: How are you using ASIO4ALL? In other words, what plugin it serves as input for? posted by TopPop on October 11, 2008 at 12:31:55:
Otachan ASIO plugin is replacement for that - and, according to many (myself included), much better sounding.

The same claims are made regarding differences between versions of Otachans driver.

The "black magic" of the Otachan versions of plug-ins is equally amazing: if you translate his developer notes from Japanese, you can see that most of his changes were in the User Interface and error-handling code, yet there are many, many posts here that discuss the vast differences between these versions of his plug ins. Highly amusing!
http://www.audioasylum.com/cgi/vt.mpl?f=pcaudio&m=41234