According to Audacity:
"MME: This is the Audacity default and the most compatible with all audio devices.
Windows DirectSound: This is more recent than MME with potentially less latency.
Windows WASAPI: This host is the most recent Windows interface, that Audacity supports, between applications (such as Audacity) and the soundcard driver. WASAPI was first officially released in 2007 in Windows Vista. WASAPI is particularly useful for "loopback" devices for recording computer playback. 24-bit recording devices are supported. Playback is emulated using this host. As a result, the playback slider in Mixer Toolbar will only scale the system playback slider's current level up or down rather than directly manipulating that system slider."
Everything between the quotes came directly from Audacity. Seems they had a lot to say about WASAPI.