Generally, ASIO is considered the best, but it does depend on the implementation of the drivers on a per-device basis. Bad ASIO and good KS implementation for a particular device may bias the result in the opposite way, so it is best to experiment with both. I have a high spec audio device, but the ASIO implementation is very basic, so I don’t use it.
I’m not sure what the W, H R parameters are, so I’ll have to set up an ASIO session and look into it. I assume it has something to do with buffers, so I’d experiment with the number of buffers you have defined in the ASIO setup (as opposed to in the BA1 app). As always, the higher the buffer count, the greater the latency, so experiment until you get the best performance. If you are streaming, latency my not be a problem, but, if you are using ASIO for video audio, the buffer count can make a big difference with lip sync.