Separate names with a comma.
In theory which one is better? Not asking about audible just in theory
If you want to know about theoretical/inaudible differences, you'll probably get more interest in your question in the rest of head-fi. That is their stock in trade. Here, we focus more on audible improvements.
Better for what? Either system can deliver high quality audio. This question literally is asking if apples or oranges taste better if it's about audio quality. The advantage with WASAPI is that it's a Windows standard and has no issues with DRM and system resources with the latest standards (it has two modes for setting a priority with Windows: Exclusive, that has less processing, vs Shared, which apart from the application's sound can also mix system DSP). ASIO is a standard for directly accessing a sound card's capability.
if your device came with asio drivers, well they're drivers given specifically for your device. not sure there is more to say.
wasapi is the bit perfect solution from Windows and it can usually work with any device. both have the same job, bypass the mixer and "talk" directly with the DAC(or whatever else).