I couldn’t find any information about how Microsoft’s Loudness Equalization works…
ReplayGain, MP3Gain, and Apple Sound Check all work by pre-scanning the loudness of the file and then adjusting the volume at playback time (or by “permanently” adjusting the volume in the case of MP3Gain). These use a loudness perception algorithm and they make one volume adjustment before the file starts playing so the dynamics of the program are not messed-with (loud parts of the song remain relatively loud and quiet parts remain relatively quiet).
Microsoft’s Loudness Equalization doesn’t seem to be associated with particular files or any particular player so I assume it’s some kind of automatic volume control. (If that’s what it is, it will continuously adjust the volume during the program/song making quiet parts quiet louder and loud parts quieter.)
Audacity’s has a Compressor, Limiter, and Leveler effects can be used to make the loud parts quieter and/or the quiet parts louder. These work on amplitude and timing without any loudness perception.
And, there is an optional [u]ReplayGain plug-in[/u] (which isn’t really ReplayGain but it uses the same/similar loudness perception algorithm ).