I should say that ASIO and WASAPI are equal from a sound point of view. If there are sound differences they are very small if any.
When using WASAPI it is important that you tick the box "Open device for exclusive access" which means that take the shortcut to your DAC not using the sound card of the PC. This is also the way ASIO is working. You can read more about this on this link:
http://wiki.jriver.com/index.php/WASAPI Please note that it is not always free of choice between ASIO and WASAPI. In my case to take an example, I use an Aesthetix DAC and they support WASAPI. When I connect the DAC and the laptop, Aesthetix is uploading WASAPI. In my previous DAC it had ASIO. If this is not clear with PS Audio, please contact them. Normally their interface should be uploaded and be visable in "Audio Device" like you see in the link below.
Another important set up you have to do you find in the following link:
http://wiki.jriver.com/index.php/Audio_Setup There you find info on how to set up Windows and Audio set up in JRiver.