Can't stop playing. D-pad when I can, stylus while eating. 

Depends which way is more comfortable at the time. So I voted both. I prefer to use the d-pad but if I'm leaning on one arm or something, I'll rest the ds somewhere and use the stylus.

Mostly d-pad. The stylus comes in handy for movement in open areas so you can take the shortest route but lacks the fidelity to navigate in cramped spaces. Never use it anywhere else, the d-pad is just quicker in the menus. It is nice to see that almost anything you can do with buttons can be done with the stylus though making one-handed play possible.

I prefer the d-pad.

directional pad

DQ IX doesn't strike me too much as a game where it's really convenient to switch between control styles, like Pokemon and Ace Attorney, simply because of the very small commands that are hard to touch in the first place, and require a double-tap. D-Pad is usually more convenient. I tried the Stylus once, but I ended  up disliking it very much.