Normally the ASIO output path will be more direct.
For example, Asus and Creative hardware require ASIO to avoid resampling.
Several other cards bypass driver audio effects with ASIO, but not with WASAPI.
However, many USB DACs work best with WASAPI - Event Style, and don't even have (or need) an ASIO driver.
So there aren't hard rules, since it varies by hardware and driver. Our general guidelines are in the wiki:
http://wiki.jriver.com/index.php/Audio_Output_Modes