@Skipii, Ken is correct that DAd and DAA are equivalent in terms of the notes and chords available. Chord voicings are a bit different; they are more compact in DAA and a bit more expansive in DAd. But you have exactly the same notes available to you in those two tunings, so any claim that one is better for chords than the other is pure nonsense.
There are two main limitations with either tuning. The first is key, for you can only play in a handful of keys (D and Bm are easy, G and Em are doable, A and F#m are a stretch, and anything else is near impossible). The second is that you still have a diatonic fretboard (which is why the keys are so limited). Fretting across the strings allows you to get around some of the limitations of the fretboard, but not all of them. Personally, I play dulcimers with both a 6+ and a 1+ fret to allow a greater variety of notes, chords, and keys. You might consider adding those extra frets as well.
The answer to your question is that it doesn't really matter. Most of us who play modern music tune to a 1-5-8 tuning such as DAd, so you will find more resources for that tuning. That might be reason enough to tune that way.
I would suggest you listen to the dulcimer players who play the kind of music you want to play and ask them how they are tuned.
Dusty T., Northern California
As a musician, you have to keep one foot back in the past and one foot forward into the future.
-- Dizzy Gillespie
updated by @dusty-turtle: 10/24/19 01:20:40AM