All depends on what you plan on doing with your DAC box.
ASIO is a low latency
driver which can give you better audio quality mainly by virtue of the large number of professional 3rd-party plugins you can get that use it.
It also allows for programming direct low-level access to audio hardware components without needing to go through intermediate processing steps. This pays off big time when you're doing something like playing a software synth through your DAC and you don't want to deal with occasional time lags that may crop up between between pressing a key and hearing the sound.
So if you're doing synthesis or sampling (especially using keyboards in real time) or you plan on doing live recording or studio type post production work on audio tracks, ASIO is probably the better choice. Especially if you want to start exploring the world of pro-audio plugins.
For simple playback, home theater, games, and much everything else, DirectSound should work just fine.
That's my 2¢ anyway.